How far under water do you have to be to be safe from a gun shot?

Not far, for normal bullets, anyway. Water is 800 times as dense as air, so if a bullet would travel 800 metres in air before being slowed to a stop, it would only get a metre or so in water. (Probably not a good comparison, as ballistics and such comes into play more with a bullet fired in air, but it gives you an idea.)

In this GIF, you can see the bullet come to an almost dead stop in just a few feet, or the time it takes to eject the shell casing from the gun:

Saying that, there is such a thing as bullets designed to fire underwater, known as supercavitating bullets. These are designed to form a low-pressure region starting at the tip of the bullet, thereby reducing drag enormously. Only the Russians are known to have deployed supercavitating weapons, including an assault rifle, the APS, for their Spetsnaz special forces:

James Bond, eat your heart out

Note the shape of the bullet, just in front of the magazine

This still has a much reduced range compared to in air, though, only 30 metres in 5 metres depth of water, 10 metres at 40 metres of depth. So, still not terribly far.

I give you the Russian SPP-1 pistol:

Again, designed to be used underwater by Spetsnaz troops. Multi-barrelled, so that the excessive length of the rounds doesn’t produce an unwieldy magazine. This is probably more James Bond’s style, I think. And, yes, it can be used out of the water: