There are many styles and types of Old Time music, with many different instrument lineups. Bluegrass as started by Bill Monroe and followed by most of the bands since who profess to play Bluegrass is a carefully arranged version of a small sub-set of Old Time music, with a standard set of instruments played in a specific way, usually non-crooked tunes and three part harmony vocal choruses. It is arranged for performance on stage as opposed to informal back-porch sessions.
Someone once said, maybe here, that Bluegrass uses a tune to show how good the players are, while Old Time musicians use their skill to show how good the tune is.
I'm a keen Old Time fan and player who likes some (the best) bluegrass, but a lot of it is a bit boring.
Cheers
Ray