Did I screw up by introducing cow's milk?

My son is 13 months old. I work full time, and I reluctantly went back to work when my son was 9 weeks old. I've been breastfeeding, but he has always taken a bottle because I had to supplement the first 10 days of his life. I pumped at work until a couple of weeks ago. I hate the pump, so I slowly started reducing pumping sessions and we introduced cow's milk for when I'm at work. He has never taken the cup well, and we've been trying since he was 7 months old. For the past month, my son has only been drinking maybe an ounce at a time from the bottle, but lately, he just pushes it away. He nurses fine when I'm home and he still wakes up at night to nurse. He is generally a good eater most of the time. We are worried about how little he drinks while I'm away at work... especially around the time that I get my period because my supply drops. Did I make a mistake by weaning from the pump? Should we have not put cow's milk in his bottles? I don't know what to do! Sometimes he will take a few sips from a regular cup (like an adult cup) but I don't feel like he's getting enough to drink while I'm gone.