What does it mean when you hear a single ring from an old style bicycle bell.

That a bell might be near by? To add to that... sounds don't have "meaning" behind them. Even if it was a spirit, which you might be implying... it doesn't have a meaning attached to it so much as it would be a spirit simply trying to get your attention.

If its doing it on its own there is a ghost

I awoke last night to my cat outside around 3:45am. As I laid back down, I heard what sounded like a Ballerina Music Box playing. I heard it, "Clear As Day."

Then, about two minutes later, I heard a bicycle bell, it rang twice. It was as if it was about three or four feet away from me.

I went back to sleep, only to dream that I had to pack some stuff away into the attic of my home. I felt the dream was telling me to go up there.

I have been experimenting with paranormal equipment lately and I'm wondering if I invited spirit activity into my home.

I do know, that a gentleman passed away in this home from natural causes about twenty five years ago. Could it be him? Could it be my mother trying to contact me?

I know it was real and I know there is a meaning behind it. I felt no fear, it was peaceful to me.

Nope, human spirits don't stick around after death. Doesn't mean it wasn't a spirit though.