"I'm dating a separated married man. I'm married. I went to high school w his ex wife 30 yrs ago. Any other questions?" she tweeted Tuesday in response to fan inquiries.
Frankel is separated from husband Jason Hoppy in 2012.
She filed to end their marriage in 2013, but the divorce is still pending due to settlement negotiations.
"The Real Housewives" star and Shields reportedly started dating over the holidays and were spotted holding hands in New York last week.
The couple are said to have gone on vacation with Frankel's co-star Carole Radziwill.
"Bethenny and Dennis seem happy together and have traveled together," a source told Us Weekly. "They have gone out with Carole [and her boyfriend], Adam [Kenworthy], and have hung out with each other's friends."
FOLLOW REALITY TV WORLD ON THE ALL-NEW GOOGLE NEWS!
Reality TV World is now available on the all-new Google News app and website. Click here to visit our Google News page, and then click FOLLOW to add us as a news source!
Frankel's co-star LuAnn de Lesseps is among those who have criticized the star for having a relationship with a married man.
The pair clashed on the June 8 episode of "The Real Housewives of New York," which airs Wednesdays at 9 p.m. ET on Bravo.
Copyright 2016 United Press International, Inc. (UPI). Any reproduction, republication, redistribution and/or modification of any UPI content is expressly prohibited without UPI's prior written consent.