The Tempsford Museum at the Stuart Memorial Hall is open on the first Sunday afternoon of each month- https://www.tempsfordmuseum.co.uk/
I would contact them about how to access Gibraltar Barn. Their website does say that, on application to the Trustees, they may be able to open at other times if requested- emphasis on the may be.
The Tempsford Church website specifically states that it is only open at service times- https://riversmeetchurches.uk/ so contact the Vicar (Revd Graham Buckle) [email protected]. to see if you can arrange for the Church to be opened for you. I see that this month (May) they had a tea and cake session on the 2nd Thursday afternoon- that may be a good time to go to the Church if it is a regular event.
The service times, in a rural 4 Church benefice probably vary each month.
Interestingly at Gibraltar Farm they is also an oak tree which is a memorial to the Polish resistance movement, another oak tree which is a memorial to two people lost in Operation Jericho in 1944 (when Amiens Prison was bombed in support of the Maquis, the French and Belgian Resistance, being held there by the Gestapo) and an external plaque commemorating another man lost in another air accident with 161 Squadron on 1 June 1944- an Arthur George Maskall DFM- that flight was supporting the Dutch Resistance Movement- https://www.roll-of-honour.com/Cambridgeshire/CherryHintonMaskallAG.html
https://en.wikipedia.org/wiki/Percy_Charles_Pickard
So there is also external material to see at the Barn as well. It sounds like someone local (from the Museum Trust) may be useful, if you can organise it, to give you a "guided tour". The sort where they do it for the love of it, and you give them a healthy donation.
EDIT- I've put a lot of material about Tempsford on the above WMO links- it has taken a lot of pulling together from many disparate sources, as there does not seem to be one place that tells the whole story. Someone could do with properly establishing how all the memorials at the Barn (and there may be others) are situationally located around the barn. Hopefully someone better placed than me can complete that story.
It seems that it is POSSIBLE to get to Tempsford by public transport from surrounding railway stations on a community bus called the Ivel Sprinter- https://www.ivelsprinter.org.uk/ Whether that could mesh with your plans is another question.