After they have bloomed for you, what are you doing with them? To keep them at a large size or to grow them in size, they need good growing conditions. Some of the bulb hybrids send up leaves with the flower stalks, and others wait until the flowering is done. Either way, this starts the growing season for your bulb.
It might be in the middle of winter and you might be in a northern climate, but this is a tropical bulb that has just finished its dry dormancy period. It needs warmth, sunlight, and enough moisture to keep the soil damp. If you only have a cold windowsill to grow it on, you need to move it back far enough to keep it warm while still giving it as much light as possible. A grow light is very helpful. Very often, the pot is small and there isn’t much potting soil—which is good, since that helps prevent it from rotting—but it does mean you have to water it often enough to not let it dry out. You can start fertilizing it with a general fertilizer as the blooms are finishing.
When the weather warms up so that there is no chance of a frost or even temperatures in the 40s or low 50s, you can move the pots outdoors. For larger, quicker-growing bulbs, take them out of the pot and plant them in the garden. At least six hours of sunlight with afternoon shade is good. Again, make sure they are watered but not too wet, or they can rot. Use a tomato or rose fertilizer following the label directions.
In the fall, as the temperature drops back into 50s, dig up the bulbs or start bringing in the potted bulbs. The bulbs can be left in pots for winter storage, but they may begin to bloom while still in storage. Cutting off the leaves and roots so that they look like the store-bought bulbs and then putting them in a cool, dark location will often work better. Check them weekly, as some bulbs may start growing weeks earlier than the eight to 10 weeks that is the normal dormancy period.
Some of the hybrids don’t grow large bulbs, and some will grow offsets or pups that become new plants. The new side bulbs will sap the strength and size of the mother bulb, but you get more bulbs. If you leave the mother plant and the side bulbs in the same pot, you can get a huge display of flowers, as each side bulb may grow a flower stalk.
You can see how I cut back the leaves and roots and how some bulbs start growing too early in storage in my video on Amaryllis Fall Care on the Greener View YouTube channel, @AGreenerView.
