yeah if you are looking to make this a full time job then you should certainly be better than competant! To play music professionally you should be a proffessional, ie know the instrument inside out, know how improve a track in any (or most) genres with your bassline's, be able to fit into any session be it reading or improvising.
To be a professional, and command professional wages, you need to be able to do it all. compare it to a professional in any other field, if a plumber turned up at your house and said 'oh... taps, I'm not that great at them...' you would rightfully be very annoyed! same with music. Technique, reading, harmony, band relationships, improv, groove etc etc should all be mastered (for as much as anything can be mastered!) before you start to sell yourself as a studio player.
look up the 'wrecking crew' if you you don't know of them already, they are a good standard for studio musicians! (if a very high one)
I'm not suggesting you are not ready, I don't know you

just suggesting to you and others who may read this thread to have a think whether you are a complete enough musician yet, a lot of people I talk to about this subject end up thinking 'no, not quite yet'. Some of them go away and practice there ass off, and then they start to get work!
If you already have a bit of work thats cool, if its a long term paid collaboration with a band then you need to make sure they are paying your living, ie if you are working with them enough to not be able to have a day job (long studio sessions etc) they need to make it worth your while for not having one, plus a bit extra for the lack of security in doing this kind of job (not to mention paying for your skills and experience) I'm not sure what that would be in the us.
In the uk I work mainly with indie labels and independent artists (I work with major labels to much in my day job



) so I don't command big bucks. I tend to charge as you say a flat fee for the first 3 hours then a fee for each hour after that.
one tip though, MAKE SURE this is all set in stone before you get your bass out of the case, some people in the music industry are sly (I've met a lot) and even more are a bit ditzy (I've met a hell of a lot

) get some contracts sorted if you can and get them to sign it early on in your correspondence!