City Manager Clint Garza said the department made the request as a precaution for worker safety on the road during construction.
The ordinance will go into effect after it has been posted by City Secretary Kaylynn Holloway in accordance with the law.
City Council and staff also discussed speeding issues on locally maintained roads, including Falcon Head Boulevard, Spillman Ranch Loop, Vail Divide, Great Divide Drive and Tordera Drive.
The Bee Cave Police Department has been conducting traffic studies to determine how big an issue speeding is in certain areas. City staff also conducted a survey of residents to gauge input on certain speed abatement measures.
Council members agreed flashing signs might be the best route—acting as a visual reminder for drivers to slow down.
Council Member Andrew Clark said the flashing speed limit and stop signs seem to be the most effective and least expensive option.
Council will later decide whether to purchase and install the signs after city staff researches their prices.