In bluegrass music, the guitar plays an integral part of the ensemble as the basis of rhythm and chord-structure for the songs.
That's one reason why many bluegrass jams tend to follow the guitarist. As bluegrass music has formed over the years, the guitar has taken on more of a role as a melody instrument as well. Due to these roles in the ensemble, bluegrass guitarists seek guitars that are loud and have a lot of bass response - for the rhythm guitar - as well as treble presence for solos to cut through the mix of other instruments.
Far Left - The Martin D-18 is an iconic bluegrass guitar. This standard model of the Martin lineup features a solid spruce top, solid mahogany back and sides, and ebony fingerboard and bridge. It is made in Martin's "dreadnought" size and has forward-shifted scalloped bracing to give it a robust sound. This guitar does not have a ton of complexity to it, so it is a good choice for the bluegrass ensemble.
2nd from Left - The Recording King RD-328 is modeled somewhat after the Martin HD-28. It pairs a solid Adirondack spruce top with solid East Indian rosewood back and sides. The Adirondack spruce is a very stiff wood that can be played hard and responds well in a bluegrass setting. The rosewood back and sides are a very "reflective" wood that add a lot of complexity to the sound of the guitar. This is another great option for a bluegrass ensemble and is another color on your sound palette.
Middle - Pono DS-20 - This is a variation on the typical square-shouldered dreadnoughts listed above. Whereas those guitars have the body meeting the neck at the 14th fret, this style moves the bridge back into a more centered position in the lower bout of the guitar. This gives it a loud, full sound but also makes the neck of the guitar shorter - meeting the body at the 12th fret. This guitar can be a good choice for musicians who want the large body size, but have difficulty reaching the neck of a 14-fret dreadnought. While it isn't as ubiquitous as the D-18 and D-28, there is some tradition of 12-fret dreadnoughts being played in bluegrass music with Norman Blake being a notable example.
2nd from Right - The Recording King ROS-11 is modeled after the Martin 000-18 and while it isn't a "typical" bluegrass guitar can be a good option for certain guitarists. It still has a relatively large body shape but the more narrow waist can make it more comfortable to play, especially for musicians with shoulder issues. It has a very balanced tone and is more commonly seen in Old Time ensembles.
Far Right - Epiphone Olympic - Definitely not a typical bluegrass guitar, an archtop guitar can be a good choice for a bluegrass jam that already has a number of guitarists. The arched top and f-holes give it a sound that is punchy and occupies a different aural space than the dreadnought guitar does. That's one reason the Epiphone Olympic - made famous by Dave Rawlings - paired so well with Gillian Welch's Gibson J-50. *It is important to note that Epiphone released a modern version of the Olympic, which lacks some of the definition of its namesake.