So my 2002 sat for 6 or 8 months and my battery died. I was half drunk and tryed to jump it from my car, but the car was running and I blew my 30amp fues (the one next to the battery).

I replaced that and jumped it from my car again (this time it was off) and as soon as it started I pulled the cables off and the bike died. So I jumped it again and let it idle for about 15 minutes and then pulled the cables and again it died. The battery is reading 6.5v, so low my charger won't even start to charge it.

so my question is, shouldn't the bike run even with the battery being dead once I start it? If so, what else could be blown?

 

No, It uses the battery and the Alternator for the electrical system at all times. Alternator peaks its 1.5-2 volt charge above 5k rpm, but battery and alternator opporate at all times. when you remove your car battery from it = irratic power spikes, the alternator charges the battery irratically, it cannot opporate the electrical system by itself.
Get a new battery and check to make sure your Regulator rectifer is not burnt. You may have burnt it out, because you had your car running when you jumped it.