The cost for Breeding Genesis and Generations Bees is based on the number of times the male Bee has been bred before.

The Breeding cost can be reduced by 25% by applying an Epic Breed Ticket during the Breeding process. Win Breeding Ticket shards by playing Game Mall games and/or participating in Raffles.

Gen Z Bees have their own Breed Tickets.  See this FAQ for Gen Z Breed Ticket details.