I tried once to share a cab with a cabin crew member , she was very accommodating but the cab driver was adamant that he was only allowed allowed to take cabin crew not cockpit crew . He suddenly changed his mind when we suggested that a good tip would be in order . Problem solved !
i do however have some sympathy with the poster ,to miss a cab by a couple of minutes is very frustrating, but starting at 6am the usual public transport is all up and running. She probably has no concept of the intricacies involved getting an aircraft from A-B . I’m sure the crew did everything to help out, but we don’t control the winds or ATC or runway in use .
Temper all of that with the fact that the cockpit crew are often on overtime so shaving 5 mins off a fight time is of no benefit to us , especially if you have been told on previous occasions that they wouldn’t share transport with you .