Would an 80cc bore kit fitted to a 50cc engine make it become a 130cc bike?

And if so would it be more powerful than a stock 125cc engine/bike as I want to add an 80cc bore kit to an aprilia rs50 and don't want to loose power but not buying a RS125 straight off.

That won't work. You should just go buy a bigger bike, dude.

Johnny hopping up an existing motor is an expensive way to make power. A surer way is to trade up. And .... no you won't have a 130cc bike after your experiment.