I am aware of nowhere in the United States that gives any exception to Bounty Hunters in the traffic law.
Trust me, he can be stopped by the police for violating traffic laws. 
Also, there is no exception in my state for Bounty Hunters carrying weapons. So if it's legal for YOU to carry a gun/baton exposed, it is also legal for him to do that. If you can't, then neither can he. At least in my state.
Someone with more info about CA law will be along shortly, I'm sure.
Sometimes there's Justice...
and sometimes, there's Just Us
1*
In memory of DCLaw- EOW@RealPolice 02-20-2007.
We won't rest 'till we find the mutt.