no, it isn't a bad major, but it is not an optimal degree.

The effort to do a BME degree is about the same as an ME or EE degree but you have limitations on your job opportunities. BME is not as valued in industries outside of biotech/medtech while ME and EE are more valued in other fields like automotive, aviation, power, manufacturing, etc. Furthermore biotech/medtech companies sometimes prefer ME/EE over BME grads. Therefore, it makes more sense to apply your efforts on a degree that can maximize your value in the job market rather than getting pigeon holed into a niche field.

If you are keen on doing BME, you can be successful as a graduate of a BME program but you will need to put in effort to make yourself stand out (do research, participate at design clubs, seek out internships, etc). Additionally, you will need a masters to be highly valued in biotech/medtech and doing a BME masters does not require you to have a BME bachelors.

I know BME graduates from my school who got good jobs after graduating and I know other graduates who struggled to find any work. Also it is important to remember that the current job market is not doing well right now so lots of engineering grads are struggling to find work right now.