Can you have a ganglion cyst on bottom of wrist under thumb? co-worker has hard bump that hurts and that comes and goes.

Yes: If sore or getting bigger see hand surgeon.

Yes: You can certainly have a ganglion cyst located in that region. This would more than likely be associated with the tendon sheath that helps move the thumb in toward the palm (flexion). These are easily treated but should be examined by a hand surgeon to make sure it is nothing else other than a typical cyst.