Yesterday I found a spot in a window that looked like water had leaked in, I started to dig out the sheet rock and found the studs in the bottom corner were rotted.  Im sure this was due to a leak we had in the roof years ago but had been fixed but I not seen this spot since my wife has layers of curtains on this window and I just never saw it from the outside. This is an upper window on a 2 story bay window and I haven't looked into the bottom one yet afraid of what I'll find.

I know I'll have to tear out some sheet rock to get a better look at the damage and have concerns since the vertical studs are load bearing.  I'm having someone come over to take a look and get an estimate on fixing this.

My question is this, will wood rot be more apparent in the cross members since the water pools here and less on the vertical studs since the water just runs down and doesn't soak into the vertical studs?  

Typically wood will wick moisture from the end grain.  So the studs may rot from the bottom up and the sill will actually have less rot.  Though every situation is unique.  In many rot situations the moisture is coming in from below and the sill rots first.  Water travels in strange directions too... You just won't know until you explore as much as you are willing.

Good plan to attack it from the drywall side, that won't take any load off.  You will need jack studs installed before you cut out any rot.  Then cut to solid wood, fit in new wood and sister stud.