You can't turn the cover bar off. But it is a good function. Keep in mind your sniper-specific skills only have to be in the cover bar. You can remove the regular skills from it. So just put things like Explosive Probe, Snipe and Ambush.
Put skills you can use both from cover and standing in the lower bar (rifle shot, Frag grenade, flash bang, overload shot etc.)
You can leave the normal top bar empty for now. Eventually you'll want to start mirroring things because you'll have skills you can use both on the run and from cover and run out of room on the bottom bar.
That's the best I can do since I never play snipers, and the only time I ever use cover as an Operative is to pop Explosive Probe so I have a lot more leeway with the top bar.
The only annoying bar is the cover bar keeps what ever keybinds you normally have for the top bar. So you'll have to fiddle and move things around a bit to get it where you like.