Well in game it really depends on you GM's decision regarding licenses. I would probably make you buy other licenses for you gear, but the bounty hunter license would be enough to let you capture and transport fugitives (which can be extremely useful with a good hacker to forge bounties).
In real life, it varies largely from state to state, but 90% of the time you have to have the rest of your licensing done separately. It's similar to a Private Investigator license, it just lets you do the job, not carry the things you need to do the job. Most states separate the licensing as much as possible so that if you're traveling to a state where part of you licensing isn't valid it doesn't drop everything (for instance if you get a concealed carry permit in Arkansas, a lot of other states won't recognize that conceal carry license if you travel to them. If it was directly tied to your bounty hunter license, that would most likely end up voided too since they are usually regarded as a binary valid/invalid rather than not/partially/fully valid.)
