I'm trying to pinpoint the correct application of the verb "to bid" in order to use it in unconventional situations
closed as not a real question by MετάEd, Bill Franke, Kris, FumbleFingers, tchrist Feb 21 '13 at 20:03
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No, it would not. Bid and farewell collocate, but bid and sleep don't. In fact, bid with the meaning ‘say, utter, express’ isn't much used at all in contemporary English, other than with, perhaps, a sense of irony.
The definition you're looking for is this one:
So you can technically wish them anything you want:
In more practical terms, the use of "bid" in this fashion is outdated, and it is not often used except to sound old-fashioned, ironic, or excessively formal.
As coleopterist pointed out, the more idiomatic use of bid with regards to sleep is "I bid you good night."