The taster sessions lose a bit of time at the start while people get used to a bike with no brakes and no freewheel. Yes, they pretty much expect you to use one of their hire bikes, although a proper track bike* can be used if you have one. Bring your own pedals (must be single-sided to avoid ripping up the track if you crash) as otherwise it's clips and straps. You also need a helmet and mitts or gloves.
I'll give them a call and see what they have available. I know the 7th October had a choice of two free 90 min slots when a colleague checked this week.
*by which I mean something with track ends, a reasonably high BB - Manchester standard is 11" but I've never seen them get a tape out - and no sticky-out braze-ons