Parrots tulips are not hybrids but tulips which have muted. The multiplicqation is very slow. If you plant a bulb now you will be able to multiply a parrot bulb in 25 years from now, separating the new bulbs.
May be the 'more experienced bulb growers' who will be along to help will tell you more.
I am growing Parrots Betty and they return each year but i do not dig them out so I did not check the bulbs.