RE: Jumpstarting from a car - You can use a car's battery to jump start a bike just fine. You want to ensure that the car is OFF, as the current spike from a running car's alternator going into recharge mode (i.e. high output) can have 'less than optimal results' for your bike.
RE: Batteries (In General) - If the battery is the "needs maintenance" type, have you checked to ensure that the water/electrolyte levels are up to the proper marks? A battery may have the voltage necessary to run some lights, but no where near the Amp-Hour (Ah) capacity to actually perform more than one start. Also most motocycle charging systems need the bike to be ridden at least 15-25 minutes to recover ONE "cold start". If you're taking several short trips less than that interval, you'll never fully recharge the battery. Repetitive discharging without recovery, and eventually you'll "kill" the battery's ability to hold enough charge to function. Its also not unusual for some bikes to need a new battery every 18-24 months (depending on their "off-state" current draw, external maintenance charging, etc.).
I'd first pull the battery and take it down to your local shop and have them check it. If you don't trust them, take the battery to a large auto repair shop. They likely have a battery tester that can be set in "powersports" mode that will test a battery that small (e.g. Pep Boys, NTB, etc.).
YMMV...
