Lil John, I am surprised to hear your bees get upset. I mow in front of entrance in the spring with a riding mower, or 40 volt trimmer, no problems. During a dearth, I wear protection. My bees are not really bothered by the noise, (gas or electric). Now grass exhaust on hive entrance is asking for trouble. My hives are 12" above ground, so actually I am mowing under the hive, not directly in front of the hive entrance. I am sure this makes a difference, also soft grass, no heavy weeds. As long as I don't vibrate the hive, my bees are usually OK.
Using an electric leaf blower, I inadvertently (the wind picked up) showered a hive entrance with leaf matter. Oh no, I thought. Now that excited the lil bees and they let me know it. However, the bees immediately calmed down after I redirected the leaves away from the hive entrance and I paid more attention to the wind gust. Gotta luv those lil critters, I say.
Blessings