Have you checked the tensioner?? Its just underneath it and will do the same thing. I have to give mine a drink of WD40 quite often. Always thought it was alt..
Is yours squeeling with the belt off when you give it a spin??
Andy is right-on. If you're losing an alt bearing, you can hear it quite easily with a mechanics stethoscope held to the alternator casing. You can carefully listen to the tensioner, tensioner pulley, idler pulley and smog pump (all of which can make noise. Smog pumps tend to squeak if they start to corrode). Do be very careful around moving engine parts.
I've got a similar squeak that goes away after the car is warmed up.
A few years back this happened and it was my smog pump. At that time, it would not spin freely or well at all. I check this a week ago and it spun ok, so maybe it's something nearby.