First and foremost, you are most likely trying to strangle the neck. Don't pull on the back so much with your thumb. Secondly, stretching isn't that necessary on bass. What's wrong with sliding your hand along?
Thirdly, you need to be asking your teacher, and if they convince you it's all needed, all well and good, listen. But actually, that stretch isn't too bad, and if it's too much, your teacher should start you on, say, fret 8 to fret 11. Unless he's anchored to playing in A. Some are!!
The process of moving from one fret to another (on the same string) doesn't have to incorporate leaving both fingers on the appropriate frets. Nice if you can, but so what if you can't? A bit of sideways movement isn't really going to marr your playing with some practice.