In this paper, we investigate the stability and delay issues of a two-user multi-access channel at the bit level. The two users, have the option to transmit at a higher rate (measured in bits/slot) separately, or to transmit simultaneously but at a lower rate because of the interference caused by concurrent transmissions. Source burstiness is considered by modeling random arrivals at the users, and the stability region in terms of bits/slot is derived. Further, we determine the condition under which the maximum stability region is achieved when both users transmit with probability 1 if they are backlogged; in this case, the stability region is shown to be coordinate convex. Then, under such condition for a convex stability region, we study the minimum delivery time problem where each user is given at the beginning some amount of data for the destination. For any initial queue size vector, we explicitly characterize the optimal rate allocation policy that empties the two users' queues within the shortest time.