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I don't know who you contact, but bike hire is mentioned on this page:
https://www.hernehillvelodrome.com/offroad
There was also a section in the rider briefing email about riders who'd hired bikes returning them after the race.
I didn't answer your schedule question I realise. There's three more races as part of the summer series on July 14th, 28th and August 4th. Entries are via the BC website:
I think you can hire cross bikes from the velodrome now.