The main issue with bottle gourd is pollination even though it produces large number of male and female flowers (generally 10:1 ratio). Pollination depends on bees. In general if the pollination does not occur, female flower will grow initially but fall off later. So if your garden is lack of bees you should go for hand pollination.
Hand pollination can be done by using soft brush. Run the soft brush on opened male flower and then on to female flower. Repeat the procedure for 2 to 3 days. (Both flowers look similar but male flower grows on long peduncle and female flower on short peduncle but it has an ovary in the shape of the fruit).
Extreme heat is the likely reason for not flowering.
Add some mulch around the base of the vine to help keep the roots cool and moisture levels up.