I may be qualified to answer this from a technical standpoint, and I'm sorry that this may go over some peoples heads... I'll keep it as simple as I can:
Jazz and Bluegrass come from different places (historically). Bluegrass mutated into it's current form somewhere in the 1800's, in the Appalachian area (think North Carolina/Kentucky). Since that is the region many Irish and Scottish settled, Bluegrass has A LOT of influence from their musical traditions. Later, Black musicians (while influencing Blues musically) added Banjo to the mix.
Cultural origins of Jazz is far newer than Bluegrass, and has it's beginnings in the 1900's. Stylistically they are different. Jazz is actually a collection of Sub-genrea, where Bluegrass IS a sub-genre (of Country). Technically, Bluegrass and Jazz both let various instruments take solos, have vocalists, have small and large ensembles, and came about from a myriad of influences from different cultures.
On Music Theory: Jazz is very complicated when talking about theory. Jazz musicians regularly used Modes (such as Mixolidyan, Lidyan, Aolean) to analyze the structure and chordal movement. Jazz can be in fantastically hard keys to play in, and often asks musicians to do things not found in any other genre.
Bluegrass on the other hand is fairly simple. Most of the musicians are self taught, but can be virtuosic. Most start playing at very early ages. Musically, Bluegrass stays in simple keys, easy to play on a Guitar (Such as G, C, D, or A), and usually, as they say, have "Three chords and the truth". In more modern times, Bluegrass has become more involved, springing up genres such as New-Grass, and Progressive Grass.
Progressive Grass is a fascinating thing. For those that are more akin to lissen to Van Halen, there is a complete Bluegrass revamp of the major Van Halen hits in true acoustic style.
First here are some examples of Bluegrass, followed by Jazz examples that MAY be close (to show similarities).
Examples:
Traditonal Bluegrass: http://www.youtube.com/watch?v=ug8p5pVsj9U [Good ol' Mountain Dew - Stanley Brothers]
Trad. http://www.youtube.com/watch?v=XdUrg2Cqxdw&playnext=1&list=PL9CC72BCEA43FC1F9 [Doc Watson - Black Mountain Rag]
Modern Day (Mostly) Traditional Bluegrass: http://www.youtube.com/watch?v=icMTVV5Lwaw&feature=related [Foggy Mountain
Breakdown - Steve Martin]
More Modern day original compositions: http://www.youtube.com/watch?v=kBPHG2K5EKQ [Greensky Bluegrass - Radio Blues]
Large Bluegrass Ensemble: http://www.youtube.com/watch?v=iy_CZDtIuz0 [IBMA winners - Rollin in my Sweet Babys Arms]
Progressive Grass: http://www.youtube.com/watch?v=4O3EvDcaegs [Van Halen Panama cover]
Jazz (not really): http://www.youtube.com/watch?v=Oxf6QuhGqiY&feature=related [Brian Setzer - Black Mountain Rag solo with Jazz influence]
Jazz (early ragtime): http://www.youtube.com/watch?v=xoilYt_LAe0 [King Oliver - Dippermouth Blues]
Jazz (Swing): http://www.youtube.com/watch?v=bR3K5uB-wMA [Glenn Miller - In the Mood]
In the Swing Jazz you can clearly see the link between the Scotch/Irish reel from Bluegrass and the Saxaphone riff in the opening.
That should give you a little taste of the differences between the two genres. I hate to say it, but compositionally, Bluegrass has more in common with Techo and Electronica than Jazz. I hope this helps! Feel free to ask more questions, or tell me to shut up... whichever!