Clarence White was like the Charlie Christian of Bluegrass guitar. He developed the single note lead style that has caught on as a staple of the genre - as you will hear now with players like Tony Rice.
The other giants of the genre who developed contemperaneously with Clarence White are folks like Doc Watson (perhaps most recognized as "the original") and Chet Atkins (AKA "Mr. Guitar.") Although Chet was not a "bluegrass" stylist so much as a complete pathbreaker for the instrument itself, his influence is felt everywhere, including in Bluegrass guitar.
Bluegrass music depends on rock solid rhythm playing. Listen to the Del McCoury band, to Mac Weissman, and Peter Rowan. These are lifelong pros who are as solid as granite. It is actually harder to do top notch rhythm playing than it is to do lead, particularly because many standards are in nearly open tunings (keys of G, C, A, D). This means that basic lead comes naturally; the backup, on the other hand, requires that you develop a very strong and reliable sense of rhythm, because everyone will depend on it. (These pearls of wisdom come from a strictly mediocre rhythm and lead guitar player...)
The top of the heap in Bluegrass is, of course, Bill Monroe. He was a mandolin player, but his band set the pace a generation ago and his tenor voice is the origin of the "high lonesome sound" that characterizes bluegrass harmonies. He is also responsible for writing the bulk of the genre himself, and he did it because it was right for him to do - it became popular many years later. Fortunately he lived a long and productive life and came to see the world appreciate his creations. Grab some old Monroe collections and listen carefully; you'll pick up the communication tricks between musicians that allow them to be up on the stage with a game of musical volleyball. Amazing stuff.
Finally, you should become familiar with the concept of the Winfield championships. Every year in September the National Flatpicking Championships are held at the Walnut Valley Festival in Winfield, Kansas. These are really international championships, and the contest is respected enough so that the winner is generally regarded as among the tops in the world. The neatest thing is that the level of competition is so high that the difference between the winner, second place, or fifth, sixth or seventh can be hard to see - and the contestants each respect the others.
Look for these names. Each is a Winfield champion.
Mark O'Connor (this guy won the championship at 14 years of age).
Peter McLaughlin
John Shaw
Mark Cosgrove
Gary Cook
Mike Whitehead
Jason Shaw
Stephen Bennett
Robert Shafer
James Gyles
Randy Rogers
Orrin Star
Roy Curry
Steve Kaufman
Of these names, some have gone on to do amazing things. For instance, Mark O'Connor, having made his mark as a premier guitarist, returned to his first love - the fiddle. He has since made or participated in over 400 albums.
Steve Kaufman runs guitar training camps at his home year round that are nationally famous and pull nationally known artists as faculty. Look him up in the back pages of Acoustic Guitar magazine. And his performance at Winfield? Well, suffice it to say that he won the title three times.
Good luck - delving into this genre of music is like striking gold. There is no end to it...
