Anna White, 36, began looking for places in July, when it became clear that schools in Bethesda, Md., where she now lives, would not reopen for in-person learning. The market she encountered was “a gold rush.”

“We would make an appointment to look at 10 houses on a Saturday and they would be gone by 9 a.m.,” said Ms. White, who grew up in Vermont and left the state to go to college.

The pickings were so thin that at one point, to her husband’s dismay, she put in an offer on a battered-looking house whose older occupant was hoping to remain there.

“I was like, ‘We can make it work, we can move into an apartment in the back,’” Ms. White said. “My husband — it was like a cartoon — he was shaking me.”