A guess: "Surface If You Can" by Terry Champagne
Here's an all-too-brief summary:
‘Surface If You Can’ by Terry Champagne: satirical tale of a couple of
grad students who rent a bomb shelter from an absent-minded heiress.
There is a surprise ending that makes this the best story in the
The story was published in a volume called "The New Tomorrows", edited by Norman Spinrad (covers for the 1971 and 1973 editions posted above), and has also appeared in the science fiction magazine, "New Worlds #192".
Does anything look familiar? The link below will take you to short overviews of the other stories that appeared alongside this one. Hope that helps.
~ Edited from The PorPor Books Blog
Edit. The originator of the question, in a comment, has requested "a sample of the text to the story in question." Here is the beginning:
Mrs. Amis felt a need. In spite of her health and wealth and elaborately equipped Bel Air mansion, she wanted to do-give-get something. So she placed an ad in the newspaper of the closest overcrowded university.
For Rent. Conv. bmb. sheltr., furn., util. pd., priv. estate, Bel Air, cpl. pref, $95., ph. 273-5840.
Here is the middle:
Allan pushed up on the hatch. It didn't budge. He pushed again harder.
"Hey, I can't get the door open." Puzzlement and caution in his voice.
Pam watched his efforts to open the hatch. Unconsciously, she turned her eyes to the dials they had stopped noticing.
"Allan, this meter reads 6000."
Allan descended a few steps and looked at her.
"Mrs. Amis said this meter measures the outside radiation." She wanted to say more, but her voice vanished.
"Do you remember hearing an explosion last night?" he asked, as if it were the most important question ever asked.
"Yes, it felt like an earthquake."
"I sure wish we had bought that radio."
"I wish we had a window. I just can't believe it."
"I wish we had more food."
Before they could ponder their situation, and long before they could accept the reality of it, a shock wave jolted everything inside the shelter. They clung together.
"What was that?"
"Probably a second wave attack--or, maybe, their doomsday bombs," he replied.
An unmeasured moment of time passed before Mr. Amis came to clean up. She had a devil of a time getting rid of the cockroaches and finally had to fumigate before she could run the ad again.
With her new tenants settling in, Mr. Amis could relax once again. Propped up on pillows, under thick blankets in a massive four-poster, she watched the maid depart. And pouring herself a cup of tea, she reached for the remote control and switched on the monitor, leaned back and relaxed.