We LITERALLY just did this last weekend! We started at Typhoon Lagoon at 9AM, rode everything and took a few laps around the lazy river, ate lunch, and drove over to Blizzard Beach around 1PM. It was more crowded at that point, but we still managed to do most everything we wanted (we started to get tired after a while -- all that intertube lugging!) by 4PM or thereabouts. The water parks were open until 7PM that day so, yeah, it's totally doable and I'd highly recommend it!
Regarding your questions... Yes, your ticket will be good for both parks. Yes, bring towels. (They charge to rent towels now.) And yes, you have to pay for your locker twice. Which sucks, and I feel like they ought to offer a "two-for" for those guests who plan to visit both parks. I'm not sure about busses, since we are locals and drove ourselves. Let me know if you have any other questions!