Somebody doesn't understand the rights and responsibilities of bail agents. They have to make sure the person they supplied bail for makes it to court and have to bring them in if bail is revoked. As such, they have more rights than police officers to catch their clients. They can enter buildings without a warrant and don't have to knock and announce. Many bail agreements, signed by the person who bail is being provided for, allow any amount of force necessary to be used to restrain or capture a client who doesn't want to return to custody.
Even with that being the case, she should have had more backup (a couple of bigger guys ready to help restrain him). He obviously didn't want to get in a scuffle with her and she clearly didn't want to get physical with him so she just goes for the gun. Like, what was her thinking going into this? "If he starts to resist, I'll just shoot him because I clearly can't stop him if he doesn't want to surrender peacefully."
Being a bounty hunter shouldn't give you free reign to just start shooting people at the first sign of resistance.