You definitely need to register with the state to collect sales tax, but check with the city or county you live in because this will vary from place to place. In some places you have to register a DBA name with the county clerk's office. Some cities have codes to follow and permits to obtain. When I ran a different kind of business (soap making) from home there were codes to follow and I had to get clearance from my local fire department to keep certain supplies on hand in large quantities. I don't think you'll have that problem with bow making though.
When I applied for a business license in my state they sent a packet of information with a list of county offices and their requirements. Good luck!