There are multiple "schools" of BG fingering, making it hard to give an absolute answer, but I was taught to hold down those extra fingers on BG as well as DB.
I started on cello as a kid, and taught myself BG while in high school. When I finally took my first BG lesson, I already owned a DB that was unplayable, so my BG teacher knew that I was headed towards the DB. So he taught me strict DB fingering. At first it was awkward to give up my 4-finger technique, but it just took a few months of getting used to. One thing that helped was that the new technique was systematic, i.e., I always approached a particular thing in the same way, so that the good things could become habits.
If I ever think that the traditional technique is slowing me down, I just watch some videos on YouTube of the great bassists.
If another teacher had taught me a different but equally systematic technique, I might be singing its praises instead.
I started on cello as a kid, and taught myself BG while in high school. When I finally took my first BG lesson, I already owned a DB that was unplayable, so my BG teacher knew that I was headed towards the DB. So he taught me strict DB fingering. At first it was awkward to give up my 4-finger technique, but it just took a few months of getting used to. One thing that helped was that the new technique was systematic, i.e., I always approached a particular thing in the same way, so that the good things could become habits.
If I ever think that the traditional technique is slowing me down, I just watch some videos on YouTube of the great bassists.
If another teacher had taught me a different but equally systematic technique, I might be singing its praises instead.