I'd have thought that the only way to keep bare soil free of growth is to hoe it / use a small fork or trowel to weed.
You don't want to put covering down, I assume, as that would defeat the purpose, but equally wouldn't want to use any chemicals that might affect the bees.
But I would just observe a note of caution: do you want to risk bee stings if you keep walking on the entrances to the nests; and/or are you likely to get bees nesting at all if it's a relatively high traffic area for your feet? Have you done the research that confirms that you are likely to get bees nesting there?