The first isn't used and the second is. However, you can talk about a "Bachelor of XXX [Arts, Science ...] degree", or simply a BA or a BSc or whatever.

In the US it's always plural. We would never say "I completed a Bachelor degree"

You can say both in my experience. I completed a bachelor degree before I started my graduate certificate course. My bachelor's degree was useful for finding a job. Useage may depend on the English speaking country you are in and the qualifications framework applicable in that country.