When I began training my bat speed was mid-upper 70's. At this point in my playing career, I had already earned All-Region honors playing for a DIII school in NY, but I transferred to a DI to literally force myself to find ways to improve. This was the case at my new school, where I was buried on the depth chart and told I needed to improve my bat speed, or I just was not going to play much.
About 3 weeks of hard work (training 6 days/week plus practice) later, my bat speed was into the mid-90's.
The exact improvement was 17 mph in 17 days. This was right before our season was starting and it took a lot of swings in the cage to get used to my "new swing."
I caught a break and was ready for it. When I got my chance to play, I was hitting the ball harder than ever and I stuck in the middle of the lineup for the rest of the season, ultimately earning all-conference honors. All of the hard work paid off.