Would it be okay for me to find another dentist to complete my bridge work?

You are able to get another opinion, but would need a comprehensive exam by a new dentist before moving forward.  

You are more than welcome to see whoever you would like to complete your treatment. Anytime I have a patient that is in need of quite a bit of work, I recommend a second opinion. It's always good to get a few different opinions to get a consensus so you're more comfortable with the treatment you're having done and it's necessity. If you are uncomfortable with who you've been seeing, you can certainly consult with a different dentist.

If you don’t believe your oral conditions needs all the work, seek another opinion with another dentist. If the second dentist ends up saying the same things as your original dentist, then you’ll know that you do need all that extra work. A bridge is a big investment. The teeth that the bridge anchors to HAS to be absolutely healthy. You don’t want put in all his time and money and then have a anchored tooth fail. Also, often when you switch dentists in midst procedure, be ready to pay more money. Absolutely OK to go to another dentist as long as you’re OK with paying the new dentist to fix or continue the work that your first dentist had started.