I travel almost exclusively by bus, and there are a few things to do.
1. Unless you're really interested, don't try to figure out the bus system. It's complicated. What I do is I go on Google Maps, and choose where I'm leaving from and going to, and then switch to the public transportation option. Then you can modify in the options what time you want to arrive/leave by. Way easier than using thebus.org.
2. If you have a cellphone with internet, you can go to hea.thebus.org, and put in either the intersection or bus stop # that you're at, and it'll give you a list of which buses will be arriving and when. Most buses have GPS, so HEA is accurate to 2 minutes.
3. If you're staying in kailua, the bus ride to Ala Moana is 45 minutes to an hour. Hawaii Kai is 30 to 45 minutes. Sometimes traffic gets really bad though and it can be longer. I only know about parking in Waikiki and Ala Moana. Waikiki is incredibly difficult to find free parking in, and Ala Moana has the huge mall there with free parking so there it's really easy. It really depends on where you're going downtown.
4. Bus rides can be long and infrequent, or they can be short and frequent, or any combination. Once again it really depends on where you'll be going and what time of the day it'll be. In most cases there won't be a significant change in the bus schedule from morning to evening. It's after 10 p.m. that the schedules start to get more sporadic.
Hope that helped, good luck.
