Does Army prefer candidates with ASI as drill sergeants?

Wow. I totally applaud your enthusiasm. However, you need to slow down juuuuuuuuuuuuust a hair and breathe for a moment. Once you make Sergeant, you will need to spend a little time in that rank IOT receive the required NCOERs (At least 1 year TIG and 4 yrs TIS) before you can volunteer.

Now, that being said. Once you do volunteer, are selected and graduate the course, it is my understanding that you will be sent to walk the Trail wherever you are needed. For example, in my Basic Training at FLW, there was 5 11B, at least 1 12B, there was an 88M...can't remember the rest, though.

Nope, that’s really it. As long as you don’t have have any type one or type two disqualifying offenses they will take you if you volunteer. Don’t volunteer until you have some more time as an NCO and are more experienced in your trade. Especially if you are trying to go to IN OSUT, that’s about the only AIT where the DS is actually the primary trainer, and the quality of training is dependent on the competency of the Cadre. Also, there aren’t many female infantry NCOs to fill all the DS positions, which is why they just take any MOS, OSUT is supposed to be manned 100% by that MOS, eventually when there are enough that will probably change.

Badges do not make the Soldier. As a private I used to think that however after I started getting schools and progressing, I realized that my character is way more important than graduating a school. Don't get me wrong I still jump at every school presented but some of the best NCO's I've known were not schooled out and everyone's career rarely allows for tons of schools. Schools that produce ASI's aren't a direct translation for a Drill anyway. Master your skill level one tasks because that's what you'll be teaching not Air Assault operations. Learn how to teach and be an effective mentor. When you went through there were still not a significant number of female 11B's of appropriate rank to pull from. Keep kicking ass and soaking it all up and you will make a valuable Drill and mentor/example for female and male trainees. Also, if you are at Benning there is a good amount of opportunity for schools (depending on C.o.C. and work schedule).