Sounds like the belt is slipping and the battery ligt comes on, can this be due to alternater bearing failure? The car continues to start for now

First of all if the belt has been slipping ,that causes the belt to get hot. Rubber belts ,after getting hot and cold too much ,makes the rubber hard and brittle and will crack and brake. The belt system has a tenisionor pulley that keeps constant tension on the belt .With the engine off pull on the belt and the belt should be hard to move . If the belt moves easy ,the the tensionor needs to be replaced with a new belt also.If all is good remove the belt and turn all the pulleys, A/C ,alt.,Power sterring,ect., To determine which pulley is not working proper

Belt slippage itself could cause the light. The alternator belt may have adjustment pulley, similar to 99" 2.7L that I have. I replaced the belt, and added tension and got another year out of the alternator before I had to replace it. Changing belt if it's worn, or adding tension if loose, may be all that you need, and should be tried before spending money on another alternator.
Add tension first, replace belt second, then alternator if one of those doesn't cure it. If you have to replace alternator, I'd have a fresh belt installed anyway.

Your description gives every indication of a worn/slick serpentine belt which very well could cause your battery light. Check the belt for wear and slick spots as well as tightness. If the belt is in good condition and is tight, investigate the terminals on the battery for tightness and corrosion. Most batteries will provide solid performance for 4 years. If the connections are clean and tight, I'd bring the car to one of the many auto parts chain retailers that provide a free charging diagnostic test. Although you're correct that a bad alternator bearing could be the issue, I'd certainly want to rule out all other possibilities before changing out the most costly.

Take off alternator and take to nearest part store they check for free most of the time when battery light comes on that's a sign alt is going bad

If it is alternator bearing failure you will hear a very high pitched whine from the alternator as it is revved, furthermore it would not usually cause loss of charging until it was nearly wrecked.
It is more likely to be belt failure. Replace and correctly tension the belt first.
I hope I have been of help but please do not hesitate to ask if you have any further questions.
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