Don`t be sorry for the flower cutting. The bulb has to grow and seeds cost to much energy from it. Beside : the seed is useless. You can`t use it to multiplicate the tulips . They use an other technic for it. And for that you also need a big bulb.
@bruni All flowers existence is to produce seeds . The problem with seeds is you never know what you get for colour or kind on the new ones . This depend on the flower the bee has visit before.