I would at some point fairly soon, sit down and figure out how many weeks before June 7th you are going to have when you can do long rides and build up saddle endurance. Unless you are capable of maintaining a 15 mph + the whole ride, with no stops and in all conditions, (which I am not), no matter how you work it, you are looking at at least 6 hours of saddle time, hard on both the nether regions and the body/core. You will probably find that in addition to spin classes and exercises you will need to spend quite a bit of time on an indoor trainer. Mind numbingly boring and maddening as it is, there is nothing like your own bike and bike seat in a stationary trainer to use to build up TITS (time in the saddle) endurance. In this case,extended time at a comfortable cruising speed, resistance and a lot of good music or videos to keep you occupied are suggested.

As I train for long distance and endurance riding in the winter, my goal is to be able to do 6-8 hours without stepping off the bike at more than 10 minutes for every 20 miles.

Admittedly I tend to do 40-75 mile long training rides at least once a week . I live in Houston and can get out since I am retired. Riding the bike is primary exercise between twice weekly training sessions with a trainer at the gym so don't get to heavy handed with it but do try to build up at least a 2-4 hour TITS time with no speed onus or penalty but simply riding in the saddle in time extended blocks before you really ramp it up outdoors in the spring.

It takes a lot off work but it is so worth it. The thrill will continue for every century you do.