FWIW - Getting the screw 'started', when loosening, is the trick.

Initially, I reverse my hand and hold the screwdriver handle like an ice-pick.

This allows lots of control and downward pressure, while giving a strong and slight twist, to start rotation.

Like 'Whig' said: Cleaning the 'slot' is important. It gives the screwdriver-blade more surface-contact with the screw head.

I clean the slot and its corners of crud, rust and debris by using Hoppe's, toothpicks, a smaller screwdriver blade, pointed leather awl, and a tooth-brush. This makes a great difference in how well the screwdriver blade fits.

An old trick is to use a small mallet and give some light taps to the 'hilt' of the screwdriver handle. This can help bottom the blade in the slot and loosen the threads a bit.

I also have a pile of junk screwdrivers, that I file to shape, to fit unusual screws.

(It is always good practice to lay and position a gun on a protected bench or table to safely support the weight and stabilize things, while you focus your attention and effort on properly removing a part).

I generally remove a rifle's Bolt, first thing, while the Arm is still assembled. (Safer and Easier)

All the suggestions have been good ones (and the voice of experience).