For Subflooring, what is the distance needed between screws

I don't know if there's something for screws in wood, as wood's a rather strange material.

For bolts into steel, however, there's the AISC Manual (no prices listed, but expect it to be in the $300+ range); there used to be a separate book on joints, so you could calculate the strength based on the size of the fastener, bolt pattern, etc. There was also a section for calculating the strength of different weld patterns.

Now, the rules for the optimal strengthy are going to be similar -- further apart will support a greater moment, so when the contact patch is a square, you want the first two to be in opposing corners. If using four, fill all of the corners. However, because it's wood, you have a chance of spliting, so you don't want to go too close to the edges. (if you have to; pre-drill).

The other thing to remember is that with screws and bolts, the fasteners shouldn't be taking the full load -- they're pulling the structural material together, so that the load's transfered as friction ... this means if you see a gap between the two pieces, you need more fasteners. If you have a really large contact patch, drop another screw in the middle.

Fasten your first layer plywood subfloor as you normally should.

The second (top) layer of plywood joints should not coincide with the joists and the second layer should not be fastened to the joists.

Article quote from - Position of Underlayment to Prevent Cracked Tile and Grout By Frank Woeste and Peter A. Nielsen For publication by the TILE LETTER Magazine (read whole article):

The 2003-2004 Tile Council of America’s (TCA) Handbook for Ceramic Tile Installation contains numerous details for a double layer wood floor system supporting ceramic tile. The thicknesses of the subfloor and underlayment are given in each case. Specific guidance on where to butt the underlayment end joints is not given for any detail. For example, for F142-03, the TCA Handbook states, “offset end and edge joints of the underlayment panels by at least two inches from the joints of subfloor panels; they should not coincide with framing below." It further states, “underlayment fasteners should not penetrate joists below." In the case of F150-03, the offsetting is not mentioned, but it does state, “underlayment fasteners should not penetrate joists below." The same holds true for F155; however, it also states, “face grain of plywood should run perpendicular to trusses, I-joists, or sawn lumber for maximum stiffness." The purpose of this article is to propose specific guidelines for the orientation and placement of underlayment, including end and edge joints, beyond the rules given in the TCA Handbook, to improve the performance of double layer wood systems. These guidelines are based on engineering science and field observations.

Also, since you will be using Ditra, make sure to stick with their guidelines for warranty purposes. Specifically see page 8 and 23 from The Ditra Handbook for your application.