Yes Bounty Hunters can legally carry guns, mace and any other weapons they deem necessary to apprehend a fugitive safely and protect themselves.
A bounty hunter can also legally shoot someone if they fear their life is in danger when they're trying to bring the fugitive in.
Bounty Hunters have just about any powers that a normal police officer would have and sometimes they have more powers to arrest you than the local police officers have.
The Bounty Hunter can also cross state lines to catch you if need be.