Answer: The ideal solution would be a mowing strip combined with a slightly raised edger to keep the mulch up in the bed. The mowing strip can be bare earth or a strip of flat brick, concrete, slate, pavers or whatever material flatters your landscape. The idea is to run your mower wheel on it, thus cutting the grass clear to the edge while having enough space for the mower to stay out of the flower bed. The slightly raised edger could be brick, landscape timber, stones, bender board or whatever material you like.
Also, you could experiment with different mulch materials to see if one stays in place better for you. Sometimes larger pieces will float, while smaller ones will compact and stay in place. Too, your mulch should not be too thick, two to three inches should be enough in summer.
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