hi. if it were mine. i would firstly paint a pva/water mix after rain. then paint it with an all weather paint. no risk to you and a perfectly good roof
I think painting might be a reasonable step to take to help keep the asbestos in good condition – but
probably only for added peace of mind. In confined places there is a higher risk of inhaling asbestos particles so the allotment's open air should reduce this hugely. Sealing with paint (not sure what type) would be an added precaution.
Blue asbestos is the type that rings very loud alarm bells... roofing sheets are white / grey and have a different particle structure (I believe) – the asbestos is harder and bonded together.
An unoccupied (2nd home) bungalow near to me was left without heating through the snow. (Clever). Pipes / tank froze, burst and brought ceilings down. For the last three days a decontamination unit with two "space suited" workers has been used to remove the ceiling material (I am guess there was some blue asbestos involved in this somewhere - maybe as loft insulation). The workers have been walking in and out of a decontamination unit (shower & air-filters) to protect themselves. (Everyone else’s insurance premiums will help pay the bill I suspect).
Some older schools still have asbestos (but not blue) in them – once used commonly for lavatory cubicle partitions (now removed), in some ceilings and as lining for fire-doors (often added as a skin to make the doors meet fire-burning time regs). Old, large boilers were entombed in asbestos – lots of it. All of these were simply painted to prevent knocks and chips releasing asbestos particles into the air. Of course, as up-dates take place the asbestos is removed… but without the need for decontamination units unless the asbestos is the more dangerous blue type or very soft and likely to send air-borne particles floating around.
The local authority can / should be able to give general advice about the law relating to asbestos as well as recommendations on how to deal with it. Asking a few questions without stating your name / address might be worth while. Better safe than sorry.
Double bagging sounds familiar for some types of asbestos.