Bad Battery or regulator?

[Super-Mario]

Ok guys been having trouble with my bike going dead, It has to be either the regulator overcharging and frying my battery, or I killed my battery by not caring for it (Im leaning towards myself). Over the winter probably about two or three months the bike sat. A couple days of riding to school, I went out into the parking lot and turned the key, nothing happened ( No lights or anything). I managed to bump start it and it ran fine all the way home. I didnt have a multi meter at the time so I just stuck it on my charger.

This worked but if I would leave the bike sit, and then go out to start it, it would start the bike but if it stalled, the battery would be completely dead again. I know its not the stator because it will run if jumped. I bought a new battery, but Im just worried now that it could be the regulator destroying it by overcharging/ undercharging.

So I just tested my old battery in the bike and it was reading 12.4v in the bike, but it wouldnt even power on the lights. I pulled it out and then tested it and just like I thought it was completely toast, read about 600mv (yep pathetic). I got a new battery and charged it with my tender overnight, it reads about 13volts.

I put it in the bike to see whether it was actually getting charged from the bike, it started at about 12.6 initially then slowly crept up to 14.1-.2 volts at idle, but would drop down to about 13.5-.6 when I revved it up, I thought it would go up when I did that. I stopped the bike because it seemed to keep creeping up at idle, and I dont know the point when the battery would start to be overcharged.

Im a total novice when it comes to electronics and electricity. I am just worried about this battery being fired by the regulator. Is there a way to test the regulator directly.

Thanks fellas!