To make it so my amp doesn't break up at all when I crank it on the clean channel? is this what biasing is?

The clean sounds I get out of my Omega HRD are beautiful, but they distort when cranked. I want to get that jazz sound at louder volumes. what can I do?

Stage Rig

Fender Strat
Epi Les Paul
Taylor 110
Boss TU-2
Omega Amps Hot Rod Deluxe (Dumble mod)
Clean/Drive/More Drive footswitch
Mid boost/Preamp boost footswitch

get a lower-gain pickup,or an amp with more headroom, you could also mic it at a lower volume into a pa system or something
"If you're looking for me,
you better check under the sea,
because that's where you'll find me..."
the easiest way would be to put in preamp tubes that take longer to break up. i think 12at7s are the ones, but i cant remember right now (its late and im tired). installing a negative feedback loop would help as well.
Biasing a push pull tube amp further toward classB (colder) will increase headroom of the power amp, clean it up a little but at the expense of increased crossover distortion, which may or may not be objectionable.
You may not like the change though.
As to changing preamp tubes it all depends on where in the signal chain of your amp it is breaking up as you increase the volume or gain, whether it's in the preamp or power amp and whether it's a master volume deal or not.
You may have to face the cold hard fact that certain power ratings in amps equates to certain limits being placed on their clean power output.