This spring I had grass sprout up all over my garden beds. Last fall I put down a 1-inch top dressing of my own compost, which was about a year old at the time. I have been doing this for several years and never had any grass grow in the beds. Is it from my compost or something else? Are there any reasonable methods to prevent it from happening again?

It is most likely not from your compost. Grasses propagate through the growth of tillers and rhizomes. The tillers look like blades of grass that grow along the surface and send down roots where they contact bare soil. In working your garden, you are taking the tillers out in your normal cultivation. Rhizomes grow laterally from the grass, underground. They then send up shoots at points along their length. Often, if you were to pull up a three- to five-inch tall shoot, you may find two feet or more of root. This root is the rhizome. Over time, rhizomes will work their way under or through most bed edging. Pulling up the shoot and as much of the root as possible is the best way to fight back. Using the types of chemicals that would be needed to kill back the grass could harm other plants in the bed, so a chemical solution would not be a good choice.