I'm wondering if there is any way to give bluetooth capabilities to something (specifically a tablet) that did not have the ability natively. The tablet in question is a cheap-as-dirt Azpen A700, it does have a micro sd card slot if that makes any difference.
Haha "install the driver", that's not possible the way people imagine it - the Android permission system doesn't foresee that, and they'd need to be specially built for the specific Android device anyway.
There's a high chance that your Android supports USB OTG, i.e. you can get a OTG adapter which has an A type socket and a micro-AB type plug. The micro-AB side goes into the socket on your tablet, the one you charge it through, and the other side accepts USB devices. USB flashmemory sticks will work, some USB harddisks will work (or they'll crash your tablet), all USB keyboards and mice should work, and some USB hubs will work. So if you get one of those adapters, and the adapter isn't broken, it probably won't all go to waste.
Whether it will be possible to make Bluetooth work over OTG, well, tough, i think it's a coin toss. There are a lot of possible failure points. For an odd chance that they haven't removed it by accident, you can try any cheap USB dongle, if you have those around, but don't be too upset if it doesn't work. These are usually based on Cambridge Silicon Radio chip.
If you have to extra shop for a module, get D-Link DBT-122. It's a bitch of a device with unusual identifier (and for that everybody who uses Windows or OS X hates it) so it's handled by the base driver, and needs the smallest number of modules to work (good for you). It's the likeliest one of all to get running!
DBT-122 is based on Broadcom chip. If you absolutely can't acquire DBT-122, try to get another Broadcom based one. They might be advertised with Widcomm software stack, which is exclusive to Broadcom. You will be disadvantaged, but you might still be lucky.
Oh, if you have kernel sources for your tablet of course, we could fix that and make even the dime a dozen Cambridge work.