The problem with a bet is what to do if you're raised; I personally would probably fold to a raise, but that sucks too. A raise will put you in a difficult situation.

And also, what will they call you with that you beat? With a pair of eights perhaps, but they won't call with a busted draw (which is the type of hand the most likely have), and it's not clear that they will call with a lower pair than eights.

An alternative play - using the above arguments and the fact that the river is scary - is to check, inducing a bluff. Now they will perhaps bet their weak hands, hoping to steal the pot with the scary ace.

I think all the alternatives bet/call, bet/fold and check/call are all worth considering. Hard to say which one is best.