Bridgestone made some good bikes in their time. I bought one in 1991. The first bike I purchased myself. You can look through their catalogs and determine what you have. Sheldon Brown has Bridgestone catalogs on his website:
http://www.sheldonbrown.com/bridgestone/#catalogues
Any pictures? If it does not have any major frame flaws, I would fix it up. But,
that is just me and I am a sucker for hard luck bikes.
If it fits you, I would work with the cave people to buy some used parts and get it back
on the road. Otherwise, see if you can make a trade.
When I get a used bike with some rust, I use a lube like Breakfree CLP to help
rehab the rusted parts. I have lubed up several rusted solid chains with it.
Think of it this way. You have a free bike. Learning to wrench on a free bike
is a good way to learn as you will probably have to work on all parts of the bike and if you screw something up badly, you are no worse off. Get a repair book or have the cave people to help you and consider it a golden learning opportunity. If you get a Huffy, you will need to know mechanic skills anyway.