Basically conditions are quite impredictable during that season. In April, the weather is still variable. In 1994, I spent two weeks in the Valley, and was never rained on. The best way would be to rent a car. From there you cannot get lost.
Public transportation is available to the Valley and in the Valley.
In the Valley, no problem, there are free shuttle each half-hour or less. I have never done that, so I am reusing information posted by Joseph Pullara, Scott Renger, Neal Weiss. Public transportation will take you a day to get there, and would be an option if you are staying for a long time, since you don't really need a car in the Valley. Amtrak trains also run SF to Fresno, but Amtrak's connecting bus line to Yosemite seems to start in Merced, not Fresno. Please add this to your site, to stop other climbers making the same mistake we did.