Could this be an issue with my scope?

I recently bought a Ruger Ultralight .308, it came with an older 3x-9x Bushnell Banner. I was at 25 yards on a stable bench and I could barely get it on the paper. I got it pretty close so I go back to 50 and its completely off the paper. Go back to 25, can't even touch the paper, It won't stop shooting left no matter where I'm and I crank it way to the right, it will make an amazing shot, next shoot, can't touch the paper. Looked the scope up and its only about 40 USD. I'm getting a new Nikon Prostaff 4x-12x anyway but is this a problem with my scope or rifle?

Guns are extremely dangerous and will hopefully be banned

Alignment is out or barrel is bent

Scopes typically don't come pre-aligned with whatever rifle you've purchased alongside it. I think you'll have to try trial and error at the range, or where ever you shoot, and realign the cross-hairs. The problem is almost certainly not the gun though

You need to get some help- locally.

Sight it in with the factory sights in order to check the rifle &ammo. If it is accurate you have taken out 2 variables. It is possible that barrel is not in line with the receiver or rifling is worn out. Re-install the base making sure it is tight and in line with the barrel. Sounds like base is insecure, rings are binding or loose, scope is broken.

Check to see if your scope rings are tight
I have had loose rings to do the same thing your scope is doing.

A POS scope. Could be loose but, that does not change a POS scope is always a POS.

First order once you are able, get a real scope, not a toy. Ridiculous to have good rifle, the Ruger you have is a good rifle. But, a piece of garbage for sights ruins a good rifle. Match that rifle with a proper scope and you have a GREAT hunting outfit.
When you get the Nikon you will see what I mean.

What do you mean by "pretty close" at 25 yards? If it isn't dead nuts on with bullet holes touching at 25 yards, moving to 50 yards isn't going to help… Will it?

Check over the scope and rings. Make sure they're installed correctly and tight. For information on scope installation search YouTube or go to a gun shop. You don't know the history of the scope so it could be damaged. Since you're getting a brand new scope, start over with that one.

Didn't you bore sight it first

Check the scope mounting rings, if they are loose that can be a problem. Usually, though, when the mounting is loose it will be all over the place and not pulling one direction. I'm going to assume it is not the shooter. That being the case it is probably something messed up in the scope. Put the Nikon on it and see what happens.