It should not affect the bees. But do you need to spray? The older I get, the less I like using chemicals. Sigh... In any event, we use a lot of it on my dad's farm (conventional agriculture). Just make sure there is no wind and mix according to directions. Use as little as possible and I would do it in the evening when the bees are in.
Roundup is a glyphosate and will be absorbed in to the plant over the evening. The product disrupts the action of a specific enzyme in plants. The manufacturer claims it is safe for people and animals, but as I am sure you are aware, it is a non-selective herbacide and kills darn near every plant.
Good luck, but I would encourgae you to reconsider. Monsanto, however, thanks you. :?