This is tough question that can only be answered when more details are provided. Was the felony committed doing something that may pertain to the business in which you would like to become bonded and licensed. Is it a minor felony or major felony? How long ago did this crime take place. Contact your local insurance company to find out.
Your company can be bonded and cannot be. It depends on the kind of felony you had. But you need to be careful since other companies may turn down negotiations with you depending on the felony you have. Also you may want to talk to an attorney or a sheriff about the situation.
Depends on the type of felony and whether you own the company. DUI or manslaughter are challenges that may be overcome whereas a felony involving theft or dishonesty may not.