If you are asking how long it will take YOU to get used to the strings, no one can answer this question but you. They may require you to rethink some aspects of you playing in both the left and right hands- not to mention pickup and amplification, and perhaps some other things too.
If you are asking how long they take to stretch in- this is another ymmv- but generally speaking a plain gut D and G could take anywhere from a few days to a few weeks to stretch in and become pitch stable...so maybe a month at the longest.
Remember that they will continue to develope character the longer they are on your bass- and you will get better at playing them too, which makes them seem to be getting better still.
Make sure your string height is appropriate!
I would think that the middle of May gives you plenty of time to figure things out...but don't just switch back to steel the night before your audition- not only will you need to re-acclimate, but your bass will as well.
My biggest concern would be to see if they expect any samples of your arco ability- if you have never bowed on plain gut before, it can be a very humbling experience.
Hopefully some others will chime in with some of their thoughts and encouraging words! Best of luck with your audition!!!
Joe