I don't think it's possible to get an accurate time-frame in regards to days/weeks/months, since Kishi very rarely gave any indicator on how much time passed at any scale in the manga. What I do know is that Sasuke obtained his MS/used it in action for the first time right before the Pain arc, and he killed Danzou/encountered Naruto immediately after the pain arc.
Without combing through the manga, the best I can give you is my personal educated guess at a time-frame—
Sasuke awakened his MS around the time Naruto went off to train to use Sage Mode. Somewhere in this time-frame is also when Sasuke attacked Bee. I would assume Naruto was only gone for a few weeks, but let's be generous and assume Naruto was gone for a full month (which is already a stretch). With that in mind, my guess would be that Sasuke went after Bee and used his MS for the first time a few weeks after obtaining it. Then the pain invasion happened, and that only lasted a day. Word of the Kage summit began immediately after the pain invasion arc ended - and by immediately, I mean within 24 hours of pain's defeat as they only just began rebuilding the village when we learned about the Kage summit. Naruto ran off to meet with the Raikage, again lets be generous and assume that trip took a week. As soon as Naruto got rejected by the Raikage, the Kage summit began, Sasuke killed Danzou, Sasuke encountered Naruto, and at that point Sasuke ultimately agreed to have the transplant. I don't recall when exactly Sasuke underwent the transplant, but I don't think it's relevant since I don't believe Sasuke used his MS again until the transplant.
All in all, by my best approximation, I would say that there was at most a month and a half between Sasuke obtaining his MS and Sasuke agreeing to the transplant.
Some things to keep in mind on that note: In that month and a half, Sasuke abused the ever-loving shit out of his MS. In a single month he most likely used his MS as much as Itachi used his over the course of his entire life. Also, something to keep in mind is (if my memory is correct) Sasuke didn't agree to the transplant because his eyes were giving out -- he agreed to the transplant because of his encounter with Naruto. Sasuke's vision may have started to get slightly fuzzy at that time, but it wasn't big enough of a concern to Sasuke to give in to the transplant.
