bigdog

What is in cultivation in the United States, and probably anywhere else outside of Thailand, is probably not 'Burmese Blue'. The true 'Burmese Blue' is a massive plant, with a pseudostem approaching or exceeding 30 feet or more. The plant sold here as 'Burmese Blue' could be Musa itinerans var. guangdongensis, and would have short rhizomes up to .3 meters long. It is a "loose" clumper, unlike var. itinerans which can send rhizomes out to 2 meters away, or var. xishuangbannensis which can send rhizomes out up to 5 meters away (!). If yours sent a pup out 3 feet away, you could have M. itinerans var. itinerans.

When it does flower, do not be surprised to see no fruits form at all. Most M. itinerans, except for var. xishuangbannensis, have female flowers that need to be pollinated in order to form fruit. Variety guangdongensis does have green to purple fruits at maturity though!

Post some pictures of yours when it leafs out.