It's no problem jump starting a motorcycle from a car or another motorcycle. No need to have the car running if using a car. I use a largish motorcycle battery in my shop to jump start bikes. I have a set of jumper cables that I made with 10 ga wire and small battery clamps, and it works great.
A common myth is that you can damage the charging system of a bike by jump starting it. Even if you do it from a running car, it's 14.2 V as opposed to 12.8 V of a fully charged battery, the jump start won't damage the bikes charging system. What damages the charging system is the heavy draw from the stator after you get the bike started. Assuming a good battery, if you are running the engine at fairly high RPM, the stator will be producing peak current for a sustained period while the battery recharges. Stators are pushing their luck during normal circumstances, and recharging a low battery can cook them. The solution there is to avoid running at high RPM for an hour or two so that the stator is producing less current.
As far as your situation goes, the boost power for cranking won't hurt a thing. It is simply substituting the power input from an external battery to drive the starter.
Now, having said all that, I recommend that you not be such a cheap bastard and replace the battery. Running a weak battery can be very hard on your charging system and you may end up replacing the battery anyway, AND replacing your stator and/or regulator.