If they're bees, they're not Bumblebees. They're more likely Carpenter Bees. The female Carpenter bee will bore a hole about the size you indicated, and about 3/8 to 1/2 inch deep into the wood. At that point, she'll turn 90 degrees and continue boring, parallel to the surface of the wood, for another couple of inches. Within this little wooden cave, she'll lay her eggs. On her way out, she'll seal the hole (to varying degrees) and leave. When her off-spring hatch, they'll bore their way out, leaving the hole open.

There's many suggestions on how to keep them at bay and away from the house. The most often heard suggestion is paint. Unpainted wood is an easy target. There are those who swear by paint, saying that painted surfaces keep the bees away. I wouldn't know that from personal experience. The Carpenter bees around here don't seem to mind the paint at all.

Try Googling for 'Carpenter Bees' and experiment with the methods of deterent you find. It can be a challenge. Haven't found one that works well, yet.

i have the same EXACT problem! my wife and i just bought our house and the carpenter bees seem to be in love with it. I called an exterminator friend and he soaked the house AND the shrubs around it. since then, i have not seen anymore bees. he did tell me that the best thing to do is to paint the cedar, as the chemicals will not work forever.

the guy i bought the house from said that he would get something from the paint store that he mixed in with the stain whenever he restained the wood. he could not remember the name of it, so i can't help there. but he did say that it would work fine for a few years, until the stain started to wear thin again.