Unfortunately, plungers are generally not particularly comfortable to utilize. The easiest way is to have the palm of your hand hold the bottom of the bell so that it rests on your hand. The wrist pivots to allow the mute to go from engaged to disengaged. If you do it that way, you'll have to worry about the horn moving less than if you were using other angles.
In general, a little goes a long way so you don't have to totally remove the plunger from the bell every time. A 45 degree angle is often as far out as you'll need to go.
One common trick for assisting with plunger work is to drill a hole through the top ring and put a string, shoestring, etc. through it. Make it long enough that your hand can fit through it but tight enough that it won't fall. That makes it much easier to not drop it. Another slight deviation from that is to make the string fairly long so that you can drop it when you're done playing and the string will slide down to your wrist. That will make it easier to switch from one mode to the other.