As you say, Miss Bingley may not be the most reliable of sources, but she writes that Bingley is actually staying with Darcy:
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She wrote also with great pleasure of her brother's being an inmate of Mr. Darcy's house, and mentioned with raptures some plans of the latter with regard to new furniture.
Georgiana, of course, had an establishment of her own (a subject that has been extensively discussed here previously), so that didn't mean that she and Bingley were living in the same house. We also know from Darcy's letter that he did spend time with Bingley during the winter, and at least saw enough of his sisters that they were able to communicate with him about Jane.
I think every indication Austen gives us is that the two were close friends ("a very steady friendship") and that would have continued during the months we don't see them. But they also had other friends too, so Bingley may very well have gone off and visited so-and-so, or done such-and-such with Darcy, and he might have done the same.
