Well, it's not a bulb, as such: Pleione orchids? They're terrestrial and do well in containers. Often known as 'windowsill orchids'.

They have green pseudobulbs which are about the size of a large olive. Plant into a normal potting mix that you know is free-draining and just cover the bulbs. Keep damp but never wet. Winter dormant and flower in spring. Quite large flowers - usually mauve, though there are other colours available.

Another possible is/are Clivia - of which there are several species. Colours range from a soft yellow to a dark red-orange, depending on the species. Again, they're not 'bulbs', although they're often included in listings of bulbs. They're probably better in a plastic container with excellent drainage - and put the pot on feet in a cachepot to disguise it. Clivias do better when they're pot-bound a bit - and getting them out of the pot one day for repotting can be a Struggle - often leading to the demise of the pot...:-(

Scadoxus is another shade dweller. Grows quite tall (3'+). Biggish pot as it has fairly thick roots similar to the Clivia.

With the shelter you've got available they might well be hardy outdoors all year.