I have actually used bermuda clippings to MULCH flower beds! One of the best mulches there is, after ground up leaves. Of course it would be possible for clippings to cause grass to grow - if they have parts of the stems or stolons or roots or rhizomes and if all the conditions are right. But the tiny amounts of clippings (which should mainly be leaf parts - depending on type of grass, height, mowing height) that might get into the beds should not be a problem. And if it is - then the tiny new grass plants just need to be picked out before they get established (which might be up to the customer or their gardener). I wonder if these beds are bare dirt? Rule one in gardening is NO BARE DIRT - all beds should be mulched - that alone should prevent the problem. And I wonder if there is a good barrier around these beds - bermuda will go under and over (and through the cracks) all kinds kinds of borders and barriers. And I wonder if there has EVER been any bermuda problem in these beds. If so, it will always be there unless it is VERY thoroughly removed - and then kept up with. If they had some kid weed it last year then there will be plenty more by now. It is very hard to get rid of bermuda in flower beds - especially if it has ever been established there. One the other hand - its no big deal - all beds require some maintenance. Many people refuse to accept that. If someone were to point to a bit of bermuda and say - See you did that, then you might dig it up and see if this looks like a new little plant or has there actually been roots under there for a while, or is the root actually extending over from the lawn (like through a crack in the brick border). Also if they have good quality garden soil in the beds, it will lift right out. I do as much garden work as I do mowing, but I know most mowers don't do beds - except maybe some mulch application - so that might be something to suggest. Mulch keeps down weeds and keeps in water. You might also be able to hit the beds with a blower after mowing if that keeps them happy.
Sounds like a picky customer.....