Yes, there is proof that the F-14B (Bravo) specifically carried AIM-9M Sidewinders in real life.
• The F-14B, introduced in the late 1980s (originally designated “F-14A+”), was fielded after the AIM-9M entered service in 1982.
• Navy weapons manuals and training documents confirm that all F-14 variants, including the B, were equipped to carry and launch AIM-9Ms.
• The LAU-7 and later LAU-138/A BOL rails used on the F-14B were fully compatible with the AIM-9M.
• Operational photos from VF-11, VF-32, and other squadrons show F-14Bs loaded with AIM-9Ms during deployments like Operation Southern Watch and Enduring Freedom.
• The missile was standard issue for Tomcat squadrons into the early 2000s and is mentioned in F-14B training syllabi.
So yes, AIM-9M was not only compatible with the F-14B, it was actively used and part of its standard armament.