well, I would think the bus would be your easiest/cheapest option. I think the only way to get from Providence to Hartford is going to be by bus anyways.

You could take Amtrak to New Haven, and change there for northbound train to Hartford. This could be faster in Thanksgiving traffic, but will almost certainly cost more. (If you take this route, get reservations. The northeast corridor trains are very crowded with students going home at Thanksgiving).

If taking the bus on Wednesday or Sunday, beware of traffic. Its virtually certain to be late arriving wherever you are headed, so plan accordingly.

Bus is going to be cheapest. Amtrak is $100 each way per person.

Another thought, if you are brave, there are lots of college kids in Boston who will be driving to West Hartford and who would have room for passengers and who would like some cash. Check with your West Hartford friends first and see if they know anyone and if not, check the colleges.

Thanks for your suggestions, everyone. I hadn't thought of posting something at colleges - I think I'll try that, since I'm not traveling alone, and have limited access to several colleges. Thanks also for the tip to beware of traffic to the bus on Wednesday.