Discard it as is. Roll it up and secure it with some string or tape.
Don't bother to put it into another piece of plastic (the bag) which adds to the plastic pollution of the planet.
Alternately, run a sharp knife down each of the rows of bubbles. Even cutting every-other row will decrease the volume significantly.
Is there a UPS store or FedEx outlet ...
I am thinking about using some kind of wire brush or metal curry comb.
There are some wire brushes in the shape of cylinder that you could simply bowl on that bubble wrap. If brush is sharp enough it should perforate the bubbles.
Please note that I've never tested that "lifehack" so it's just a guess.
If you have some wood outside that needs some protection, old motor oil is cheap alternative for store bought wood preservers. I am not any kind of wood working professional so check other sources about this.
I have a small wooden fence protected with old motor oil in my backyard and it holds great.
Here is a video of someone using this technique.
It is possible you don't need to change the engine oil as often. For some reason, many Americans think they need to change the oil every 3000 miles when the manufacturer's recommendation is more like 15000 miles. So the first step to reducing waste is to check what the manufacturer recommends.
Many modern cars have a function in the engine management ...