Not sure what you mean by "stakes" in relation to flowering. What species of tree(s) are you referring to?

There are hormonal or growth regulator sprays available that will stop trees from producing fruit (effectively sterilizing the flowers) but none that I am aware of that will actually prevent flowering. That is a basic biological imperative for plants - the need for reproduction - and I believe preventing a tree from flowering at all would have a impact on its health and lifespan.

But not all trees flower heavily and most do so for a rather short time frame. And some flower in such a manner as to not attract pollinators like bees (eg. conifers). And you can always prune off any flowers before they develop fully (in the bud stage) if you wish.

The good news is that bees are not interested in you. If you leave them alone to do what they do, they will not bother you. Just avoid planting anything that attracts a lot of bees close to any sitting or outdoor entertaining areas or close to walkways. And keep your epi pen close!! I am not allergic but I have gardened in and amongst bees all my life and have never been stung........except when I disturbed a nest of hornets that had taken up residence in a birdhouse. But hornets/wasps are not particularly attracted to flowering plants - they are omnivores and seek out other insects, garbage, roadkill and fallen and overripe fruit or vegetables to feed on.

What type of tree?