Thanks for the info Mike, unfortunately the e mail arrived whilst we were away !!
We decided to catch the shuttle to Zion from Springdale - dead easy, they came frequently and it was only a matter of a few minutes before they arrived at the park. It was just as well as there was NOWHERE to park around the visitor centre or around the entry to the park. Whether this was due to the time of day (around lunchtime) or it was just plain busy, I don''t know. We then jumped onto the park shuttle (after paying the entry fee of course !) and did the tour, hopping on and off as we felt. Again no problems, the shuttles were frequent and we had no trouble getting on any of them.
In Bryce we had no trouble at all parking anywhere in the park and thoroughly enjoyed it. Hiking down some of the trails was amazing. We did stay at Ruby's Inn, just a mile or so straight down the road to the park and couldn't have been more convenient.
We also managed to fit in Arches, Dead Horse Park and Grand Canyon North Rim, so in all we had a fantastic couple of weeks.
Back to reality with a bump ..........!