How does the pressure at a point in a fluid vary with the depth of the point below the surface of the fluid? A bottle, full of air at atmospheric pressure, whose volume is 500 cubic centimeters, is sunken mouth downwards below the surface of a pond. How far must it be sunk for 100 cubic centimeters of water to run up into the bottle?

Is there a hydrostatic equations for finding the pressure outside of the bottle?

we'll use Boyle's Law pV=k to solve for the inside but do we need to arrange: p=k/V?
Would we use the universal gas constant for this: 8.31432
So
p=500/8.31432 = 60.14 for inside pressure?

I'm kind of stuck on this one..

There is indeed a formula for that. Try using:

P = h\rho g

where P is the pressure of the liquid
h is the depth of the liquid
rho (\rho) is the density of the liquid
g is the acceleration due to gravity.