Can I use roof paint on a wooden table

[Whatisapension]

I found an old folding table, left by the previous owners, which would make an ideal potting table. The table top is made up of those thin sheets of wood (like cardboardey wood, I think is the technical term), with veneer on the surface which has mostly peeled off.

Could I remove the veneer completely and just paint the wood with bitumen paint? I don't need it to look great, just weatherproof and not peeling.

Would I need to do any prep work or can I just roll the paint on?

Failing that, any other relatively cheap ideas?

Sounds like it is a plywood top that is de-laminating and was not intended for exterior use. It will only get worse but for your purposes it probably doesn't really matter. The longer term solution would be to replace the top with something like tanalised timber or metal.
I'd paint it like you suggest while I think what I want to do.

if you want to make a potting table...

if it's indoors in a shed, you can use WBP ply, and paint it or cover it with something waterproof. You can also use a piece of kitchen worktop. If you cruise the DIY sheds you wil often find a damaged length greatly reduced.

If you want to use it out of doors, I think Decking Boards make an excelellen top, frame and legs. You ought to soak the cut ends in wood preserver, but if you only want iot to last a few years, give it a couple of coats all over fince fence stain.

It is very strong, quite cheap, and built to withstand outside use (apart from cut ends especially if they are in contact with the ground, concrete of paving)

You may need to buy a saw and a drill

this is an example of cheap ones that are good enough for a potting table. Sometimes they will be on clearance at the end of summer. 1800mm (six foot) is the shortest normally sold. You could saw boards in half.

I have been using some as a workbench in the garden today, laid over plastic trestles. (aldi sometimes have them in the junk aisle)