OK, let's dispel some misunderstanding.
First, a battery is considered fully charged at 12.6 volts (or 2.1 volts per cell x 6 cells - so a 6 volt would be 6.3 with 3 cells). A battery is considered fully DIScharged at 12.43 volts. Keep in mind that doesn't mean a vehicle won't start with it lower but your odds quickly diminish and the batteries storage is minimal at that point.
Cranking voltage needs to stay as high as possible but 9.6V is considered to be the cutoff point that below that the battery is either discharged or bad. Our bikes electrical system actually needs more voltage then that to even turn on the CDI/TCI. If can crank over just fine but not start.
As long as your jumper vehicle is a 12 volt system and also in good condition (not overcharging/bad rectifier) then you can jump with it running but this could potentially have a bad side effect on the battery and some even say the motorcycles charging system (though I disagree about the charging system part). Still, a safe bet would be to do it from the vehicle not running or a very short duration with it running if needed. We regularly jump with a high output starter/charger but avoid extended durations on 15 amp or higher (we have used as high as 250amps without any problems for short durations).
Now, as has been pointed out if the battery is a lead acid battery (which most are) then you can examine and refill the fluid and recharge the battery if it's low. This may or may not help it. When they get low they tend to overheat the lead plates causing warpage and shorts internally. A lead acid battery is common to go bad after a year or two. Some last longer and the more often it's used usually will let it live longer.
A gel/AGM (absorbed glass mat) battery will usually have more power and last far longer but cost twice as much. If you are going to be keeping the bike it's worth the effort required to find one (see our website for how to put in an oversize battery if you want but the noted PC680 battery works well and is a direct replacement - slightly smaller then the OEM battery but still stronger).
I've attached a great .pdf that can help with your electrical system woes.
http://www.aa1car.com/library/voltage_drop_testing.htm