Upvote:7
No, a visit to the Bahamas is not going to "reset the clock", since they're included in the Adjacent Islands zone:
Anguilla, Antigua, Aruba, Bahamas, Barbados, Barbuda, Bermuda, Bonaire, British Virgin Islands, Cayman Islands, Cuba, Curacao, Dominica, Dominican Republic, Grenada, Guadeloupe, Haiti, Jamaica, Marie-Galante, Martinique, Miquelon, Montserrat, Saba, Saint-Barthelemy, Saint Christopher, Saint Eustatius, Saint Kitts-Nevis, Saint Lucia, Saint Maarten, Saint Martin, Saint Pierre, Saint Vincent, Grenadines, Trinidad, Tobago, Turks and Caicos Islands, Other British, French and Netherlands territory or possessions bordering on the Caribbean Sea.
So you'd need to go to Central or South America instead. Try Costa Rica?
Also, the 90-day rule is for entries under the Visa Waiver Program (VWP). ESTA is just the preclearance that lets you fly to the US. See this answer to a similar question for a more detailed explanation.