The finger bones of your hand would be driven by the data glove, but would they be driven kinematically or dynamically?
Kinematic objects are guided by external logic (keyframed path, script, or perhaps real-time data acquisition) and can bump other objects that are dynamic, but cannot be influenced by these collisions (at least not without much custom special case code). You know those moving platforms you might see in a game level? They move along scripted paths and nothing can stop them -- they are kinematic.
Dynamic objects react to collisions, but can be guided by: Constraints, Actions, or external forces (keyframed, scripted, or perhaps real-time data acquisition) but their final motion is a mixture of intended position and the things that they collide with. If you want your fingers to bend or wobble when bumped against obstacles they would have to be dynamic.
The question is important because the answer would determine the strategies you could take to achieve your goals.
If you want to go Kinematic then the best approach would be to use a distinct btRigidBody for each finger bone. Slam the positions and velocities of each bone according to the data from your data glove. It is better to use many btRigidBody's because if you tried to use one you'd have to change its shape in order to articulate your hand, and changing the shape of an object can be problematic in Bullet -- you have to reset cached bounding boxes in the broadphase and destroy existing btContactManifolds each time you change the shape else risk buggy collisions.
If you want to go Dynamic there are two ways forward:
(1) Using a distinct btRigitBody for each finger bone you could connect the bones together using Constraints. You would need to push each finger toward its target position by computing the required force + torque each frame (note the proper calculation of these values would be a little tricky in order to achieve stability, but there is more than one way to do it). You'd probably want to step the simulation faster than the default 60Hz since you would have many joints (about 15).
I once made an experimental jointed humanoid character that used a variation of this strategy. You can find a video and Demo code links
this thread.
(2) Using one btMultiBody with many parts. I'm not familiar with this feature set of Bullet, but the capabilities are there and I believe they would work for a hand. Bullet's MultiBody Demo would be a good place to start your research into this method, but it only makes a long chain of parts rather than a multi-pronged joint like the palm of a hand.