The B160 visa can be obtained by filling out the DS-160 online application available through the U.S. Department of State website , which lets people apply for temporary visas to the United States. There are many of these visas, also known as nonimmigrant visas, including visas for tourism, temporary employment, study and other business purposes.
I notice you are from the United Kingdom (UK), so maybe some translation is useful for Americans to understand what happened to you in the UK.
What is ABH?
Actual bodily harm (ABH) is a criminal offence under Section 47 of the Offences against the Person Act 1861.
Assaults which are described as actual bodily harm cause injuries which are serious but don't cause serious permanent damage to the victim - for example an injury which requires stitches.
The perpetrator also doesn't necessarily have to intend to cause an injury - they only have to intend to apply unlawful force. This is known as committing the offence "recklessly", as opposed to "intentionally".
For example, if a person pushes another person and they fall causing an injury, they can still be convicted of ABH because they intended to push the person.
What is GBH?
Grievous bodily harm (GBH) is a criminal offence under Sections 18 and 20 of the Offences against the Person Act 1861.
It is a more serious crime than ABH, as committing GBH means causing really serious injuries which severely affect the health of the victim, such as broken bones or permanent disfigurement. It's the most serious form of non-fatal assault.
Unlike ABH, there is a question of intent. Section 18 GBH offences involve some aspect of intent, while section 20 offences are still unlawful and malicious, but lack the intent to cause really serious injury.
Intent can be shown through, for example, threats, deliberately using a weapon, or planning the attack.
Crimes that will make you Inadmissible to the U.S.
Below is a very basic list of crimes that will make you inadmissible to the Unites States. This list is by no means complete. You should also note that not all of these crimes require an actual conviction in court to make the applicant inadmissible.
• Crimes involving moral turpitude. This includes any attempt or conspiracy to commit such a crime. It excludes crimes committed when the person was under the age of 18 years, so long as the person was released from jail more than five years before applying for a visa or other immigration benefit. It also excludes crimes for which the maximum penalty did not exceed one year in prison and the person was not, in fact, sentenced to more than six months in prison. See the more complete list of crimes of moral turpitude below.
• A controlled substance violation according to the laws and regulations of any country. This includes trafficking and any conspiracy to commit such a crime. This includes a single offense of simple possession for a small amount of THC residue or for “drug paraphernalia.” It also includes the spouse, son, or daughter of the inadmissible applicant if that person has, within the last five years, received any financial or other benefit from the illicit activities, and knew or reasonably should have known where the money or benefit came from. No actual conviction is required to trigger this inadmissibility.
• Convictions for two or more crimes for which the prison sentences totaled at least five years. It does not matter whether the convictions came from a single trial or whether or not the offenses arose from a single scheme of misconduct.
• Prostitution or commercialized vice.
• A serious criminal activity for which immunity from prosecution has been received
• Human trafficking offenses.
• Almost anything that has to do with money laundering.
• Do not even attempt to enter the U.S. if you have been previously deported without a proper visa. This is considered a serious felony under U.S. law and can result in extended jail time.
Crimes of Moral Turpitude
The definition of moral turpitude is very broad so we are listing the most common examples of this type of crime below. The actual offenses are ever changing. Some of them may be minor such as shoplifting, while others can be very serious such as murder. The actual penalty for the conviction does not matter.
• Passing Bad Cheques
• Assault Causing Bodily Harm or With Intent to Cause Harm
• Assault with a Weapon
• Assault with intent to cause bodily harm
• Aggravated Assault. “Aggravated felony” is even worse, though these also have a very loose definition, therefore the offences can change over time. However, there is absolutely no relief, and anyone deported or excluded for this reason cannot ever enter the US.
• Sexual Assault
• Trespass with Intent to Commit a CIMT
• Endangerment and Actual Injury
• Child Abuse in some cases
• Benefitting from illicit drug trafficking.
• Prostitution and commercialized vice.
• Involvement in serious criminal activity, where the person has asserted immunity from prosecution, departed the United States as a result, and not subsequently submitted to the jurisdiction of the relevant U.S. court.
• Human trafficking, whether inside or outside the United States.
• Laundering or aiding or abetting monetary instruments.
Crimes that Should Not Prevent Entry to the U.S.
Not all crimes will result in being denied entry to the U.S.
• Crimes that are not considered moral turpitude include where the individual has committed only one crime of moral turpitude, and:
o the crime was committed when the individual was under 18 years of age and the crime was committed more than five years ago
o the crime did not exceed one year of imprisonment
o if the individual was convicted of the crime, but the individual was not sentenced to imprisonment for a term greater than six months
• Offences like fail to appear, causing a disturbance, common assault and impaired driving are not ordinarily considered in determining your admissibility to the country. In addition, multiple convictions involving crimes which are NOT classified as crimes involving moral turpitude ordinarily do not block your entry.
• The U.S. does not deny entry to persons with a conviction for “Driving Under the Influence” (DUI / DWI) despite how seriously Canada takes this type of offense. However, if there are multiple convictions for this and or other misdemeanors, you could be denied entry.
Summary - Your Visa Should Be Approved
So, you should be fine to get a B160 or DS160 visa to visit the USA. Although you caused bodily harm, it was without intent, which is more akin to an accident. You were not sentenced to more than 6 months for any one of the convictions, and multiple minor convictions do not make you inadmissible. Thus, the US Dept of State definitions of crimes of moral turpitude do apply to your two ABH convictions.
No Visa Needed
Finally, if you are a UK citizen, than you may not need a visitors visa at all. You could travel to the USA for 90 days under the Visa Waiver Program. Travelers seeking to enter the United States for business or tourism (B-1/B-2 visa), or in transit (C-1) for less than 90 days may be eligible to travel to the United States visa free under the Visa Waiver Program (VWP) if they meet specific requirements.
The Visa Waiver Program cannot be used if your purpose of travel is to study for credit, employment, work as foreign press, radio, film, journalists, or other information media, or take up permanent residence.