It's a hardy geranium, Geranium himalayense 'Birchs Double', therefore a herbaceous perennial, not a bulb. To get a true BD you'd need to purchase a plant from a reputable seller. Many companies which specialise in bulbs here also offer some hardy perennials but I'm afraid I can't help you with US sources.

What flora said :-)

Michigan Bulb sells a lot of plant types other than bulbs but has a terrible reputation in the world of mail order. Avoid at all costs!

Joy Creek Nursery has an excellent reputation and carries this plant, although it is currently sold out for the season. Thompson and Morgan also carries the seed.

Here is a link that might be useful: Joy Creek Nursery