We were a bit surprised how disorganized the whole operation was after reading many positive Tripadvisor reviews. Purchasing tickets on my phone was easy, but we showed up at one of the stops (The Franklin Institute) and waited and waited and waited, but a bus never showed up at the time mentioned on the website (50 minutes after the hour). We waited another 30 minutes and saw a Big Bus go by, but it didn't stop!
It was a nice day and we had already purchased the tickets, so we decided to walk the 1.3 miles to the Big Bus route starting point (Stop #1 - Independence Visitor Center) to see if we could figure anything out. When we arrived around 5pm, a bus was pulling in and they told us it was the last one for the day (despite the bus schedule saying that on Saturdays in the summer the final bus would depart at 6pm!).
We happened to run into someone else having the same problem who had learned on their own that the Big Bus passes work on the Sightseeing Tours busses, so we ran to to a stop in the middle of their route and the Sightseeing Tours bus actually stopped and let us on!
The tour (the remaining part we got anyway) was nice - nothing spectacular, but it was a good way to see the city.
It is still unclear why 1) the Big Bus busses didn't stop at the "Stops" mentioned to check for people who wanted to hop on, 2) why the schedules posted on the website were not even close to what was actually followed, and 3) why no one told us that our passes got us onto the "Sightseeing" tour busses which were different than the Big Bus's.
Will be looking for another hop-on/off bus company when visiting other cities!