The "bulb" is known as a tuber and you should just leave it in very fast draining soil. Many Alocasia species go dormant and when the time is right they will return. If the soil you have remains soggy then add a little peat moss and some orchid bark so it drains faster. On the advice of the aroid staff at the Missouri Botanical Garden I also cut sphagnum moss into tiny shreds and also mix that in the soil.

Don't allow the soil to become super dry but don't keep it soggy wet either. Keep the pot near semi-bright light and you may well have a new plant sooner than you think.

I've had them go dormant for months at a time and then finally come back up. In a few cases they've been dormant for well over a year. As long as the tuber is not rotting it should regrow. But just to be safe sprinkle it with cinnamon which works great as an anti-fungal.

Thanks very much for the information. Tubers are in a peat-based mix, barely covered.
I've had some success with Alocasia 'Frydek' this way, a few of them are sprouting.
I hate to see healthy plants hang around inside the box stores, (especially those that might need special care) knowing that they are surely going to become very unhealthy or die unless someone snatches them up while they are still in good shape. Wish I'd bought this while it was healthy!

There are many commercially created names for hybridized Alocasia that are very similar and likely one and the same. Aroids are extremely variable in appearance and don't always take on the same leaf shape so growers love to give the shapes a new name so they can try to sell more product.

All are very similar to a plant that originated as Alocasia Amazonica. Alocasia Amazonica is a hybrid of Alocasia watsoniana x Alocasia sanderiana although some growers believe the plant was actually a cross between Alocasia watsoniana x Alocasia nobilis. The closest species plant is likely Alocasia longiloba which used to be known as Alocasia watsoniana. Alocasia watsoniana was sunk into synonymy with the Alocasia longiloba as a result of being published to science first. That determination was made by Australian aroid botanist Alistair Hay who likely knows more about Alocasia species than anyone else.

Alocasia Amazoniica, Alocasia Polly and Alocasia Frydek are commercial names(not species names) for plants that are almost identical. In the past it was also sold as Alocasia 'Maxkowskii'

My only suggestion would be to plant the tuber a bit deeper. I have a bed of them in my Exotic Rainforest atrium and not one came up this year. Last year the bed was full. I've seen this happen many times before so if the plant is slow to come out of dormancy don't give up.

The link might help and includes a second link which explains natural variation in aroid species. Natural variation is extremely common and the basic rule is just because a leaf looks a little different does not mean it is a different plant.

Here is a link that might be useful: Alocasia Amazonica

My prettiest Alocasia Polly leaves which I got from a local grocery store did very well in Winter months, with indirect sunlight.
Come spring the plant's leaves are falling one by one. So where do I leave the tubers? in the same port or in the soil outside. I do not have a green house.
I understand I should not over water it but how do I care about the tubers to re-bloom?

I just leave mine in the pot and water it about a third as often as I would if it was in a growth cycle. When they start growing again I go back to regular watering.