I tried looking in the internet but could not find any appropriate answers.
There is no commonly understood difference in the practical meaning of the two sentences.
But since you're asking specifically about grammar, there is a possible difference in their theoretical interpretations.
In both possible interpretations, it's not a bell itself that's making noise.
- I was woken up by a ringing bell.
This could mean you were woken up by a bell designed to ring. In other words, ringing could be interpreted as an adjective (attributive noun) rather than a verb. In this case, somebody could have picked up the bell that was designed to ring—but which was currently silent—and hit you over the head with it. (Perhaps it was an electronic bell and its battery had run out.) It wasn't actually ringing that woke you up, but the bell-designed-to-ring-but-which-was currently-silent hitting you on the head that woke you up.
- I was woken up by a bell ringing.
In theory, a bell ringing could be some kind of ceremony or activity (like a house sitting), and it's being used as a noun phrase. So, those people involved in a bell ringing (bell-ringing ceremony) woke me up with the swishing of their robes.