All APOs were commissioned on getting their Cadetships, and Mark Bowman obviously got his in 78, graduating in 81 from his Aero Eng degree (if memory serves) at Imperial. Then IOT as normal.
Unless he'd joined the RAF as a Halton Apprentice at 16, a join date of 1976 is impossible, and I'd suggest that it would be entirely impossible for a 'Brat' to gain sufficient qualifications to win a place at Imperial AND get a cadetship in just two years, and had he been an ex-Brat, I suspect that fact would have been widely known.
But the compelling thing for me is that Crossbow does not come across as being a punchy, immensely likeable and sociable, academic high flier. Mark Bowman is/was - though as a VR who was younger than him, we didn't have a lot in common, or much contact.