DD has been for 3 sessions now and they still haven’t finished going through the ‘assessment’ paper.
be that the tutor is using the assessment paper to teach the methodology for each type, in which case it might take a while. On balance though, covering fewer than 80 questions in 3 hours doesn't sound good ...
Yesterday they showed me a question they had been working on and it was about identifying the word that would appear 3rd if they were ordered alphabetically. I said that I was surprised as I didn’t think it was one of the 21 types – she looked blank. Am I unnecessarily concerned?
... and nor does that. You and Y are of course both correct that the IPS book covers all the types for Bucks.
Do you know which books she is using? It could be that she is using Susan Daughtrey's Books 1 - 4. Some tutors fall into that trap because they know that Susan has a big tutoring operation for the Bucks 11+, and therefore they assume that her all her materials must be appropriate for the test.
Hopefully someone will be able to PM you with the name of an alternative tutor. Otherwise I am afraid that it may have to be either DIY, or show the tutor the IPS book and ask her to teach only those question types. I have known parents who have done that, and the tutors have recognised the error of their ways, but this one sounds terribly slow as well. I know that Patricia covers all 21 types comprehensively in around 6 lessons!
Good luck with it all.