I'm not sure about skinneri...never grown it. But here are some observations from those that I do grow..
C. aclandiae: blooms on new growth as soon as the leaves unfurl
C. aurantiaca: produces several sheaths over the summer on multiple p-bulbs that bloom in the Fall
C. intermedia: blooms on all new growths produced over the summer and winter in the spring.
I think they're ALL different in growth habit, Julie.
Back to C. skinneri...
I think it would bloom in season on all the new growths produced during active growth...that's why you see such huge multi-lead specimen plants in spectacular bloom!