Just make sure the asbestos is properly sealed in. It's only dangerous if if starts to break up, so you're at no risk providing the metalwork is solid around it. I've been following a group rebuilding a railway carriage after asbestos (used as insulation in the 1950s) was removed from the sides. It was fine until the outer body skins developed corrosion holes, at which point they had to call the hazmat team in.
Ebay gear sales can be a source of neat small bags. I bought a near mint MX last year which came with an external light meter, mint and boxed generic flash...and most usefully of all a neat little black leatherette shoulder bag. It's just big enough for an MX, 28/50/135mm lenses, a small flash and a couple of rolls of film, nestles under your arm when carried and can be slipped under the car seat if you have to stop for a few minutes and don't want to take it with you.