Aw Cindy, you aren't a bad mum.
That's very similar to what happened when I had to put Milo on to formula.
I'd been trying for ages to get him to have EBM (or anything) from a bottle, and he was getting more and more unsettled in the afternoons and at night.
One day he had a breastfeed, both sides for at least an hour, sounded like he was feeding well, then I offered him the bottle, and he drank 210ml formula.

It was really hard for me to take, but you know what, I did the best thing I could for my son, and that makes me a good mum