My mum is a little old fashioned in this sense as well. I think if I was around other people I would prob wear a bikini top over my belly with my bikini top underneath but thats because I dont like showing my tummy off normally. I think if I was just around family mum wouldnt bat an eyelid but I think if I was around other people she would prefer me to a little more covered up. Not because its 'dirty or vulgar' just so I didnt make other people feel uncomfortable.