So in a year or two when the returns of mining bitcoin reach zero, what's going keep bitcoin alive when there is absolutely no [monetary] incentive to compute the hashes?
There will always be incentive to mine. Bitcoin mining rewards consist of two things, the block reward (currently 25BTC) and transaction fees. Transaction fees are fees that are applied to transactions that are considered "spammy" and use lots of network resources, at the moment they're set to 0.0005BTC per KB on spammy-looking transactions.
Block rewards halve every 4 years, so they won't hit 0 for over another hundred years. Transaction fees will get bigger as Bitcoin gets more popular & the number of transactions per block grows so its hoped that transaction fees would help offset the halving.