Try your best to always hold the slide with two fingers and a thumb. Your middle and pointer finger should rest on top of each other at the bottom of the brace on the slide. Your ring and pinky finger should be right under the slide with your palm facing your body. Many players who don't do this have a bad habit of constantly switching their hand position or reaching for the bell as they pass by third position. Even players who don't actually touch the bell sometimes reach slightly. Either way, you should aim for your grip to be consistent as often as possible. Obviously, depending on the length of your arm, this may change slightly when you reach sixth and seventh position.
A good way to train yourself to hold the slide properly is to hold a coin against the slide brace with your two fingers. The moment you stop holding the slide correctly, the coin will fall. Do this for a few weeks until you feel that this new way of holding the slide is now comfortable. I think you will be happier with the consistency of motion and accuracy of your slide movements.