Flew on the Baby Bus just the once (well twice including the return leg) during the second week of the London Olympics in 2012. It was the closest I got to physically being at the stadium as we climbed and turned away over the Olympic Park leaving LCY. I really liked it especially as in those days one got F TPs although I have to say one felt the bumps a bit more on the crossing. On the return leg one of our fellow FTers almost fell down the stairs on disembarkation trying to get to some photos. I think in the subsequent discussion thereof here it turned out there was another FTer on board too. Unfortunately, living on the other side of town, LCY is not really practical for me, but I was glad to have done it.
Over the years there were a number of other All Business services that we tried - MaxJet (not great) ex STN and Silver Jet (they tried hard, but LTN was a killer) and one other who's name escapes me...