Typically studs are spaced 16" on center but that's a general rule that can change. It's hard to find studs behind tile as you're figured out. Assuming 16" OC you can angle the bar to hit both studs.

You can use toggle bolts and they'll probably be strong enough. You need to apply some back pressure as you tighten the screw. In the case of several in the same bracket, you need to apply some pressure and tighten each screw a little at a time.

They also make special holders for grab bars. Off hand I can't remember the name but their quite heavy duty and unfortunately rather expensive (although far less expensive than a fall and trip to the hospital).

Pull back slightly on the screw while turning it with your fingers.

When the toggle starts to make contact with the plaster, use a screwdriver for the last few turns.

Make sure no one EVER grabs the bar and pulls (even for balance).

The toggle will pull through pretty easily.

A more solid installation is to open the plaster wall, put some 2x blocking in, then repair the plaster.