I have found a TON of bulbs in grass, including daffs. The grass here is an amalgam of different types & I'm sure Bermuda is one of them. As long as you don't mow when the buds are popping up, that should work fine, but the show might not be what one would get from the same UNmowed bulbs.
But, would it not be more fun to have "a flower bed?" If you lay a smother now, the grass should be dead by spring. Newspaper won't cut it, but cardboard, sheet metal, plastic, or even a really thick pile of leaves would work. Use a straight shovel to sever all connections (stems/roots) around the edge of the spot, going about 4" deep should accomplish that. Then, if you use a solid border a few inches wide, like bricks or landscape timbers, you can keep the grass out reasonably easily. LMK if you want more info about starting/maintaining that!
