To an extent, the nature of your conviction will have a bearing on your ability to get a business loan, but you won't be surprised to learn that this can be difficult. The interest rates can also be expensive relative to those available to people without the same history.
There are specialist lenders, known as responsible finance providers, that work in local communities to help people get back on their feet, perhaps after a custodial sentence, and it could be worth talking to them first.