--it sounds like it's time to go gluten free, if you haven't already. (I sort of suspect that by posting in this section you sort of suspected that as well.)

The Transglutaminase IgA assay, at least in the presence of normal levels of IgA, is the most specific blood test for frank celiac in that it it the one most associated with villious damage, which is why the bowel biopsy is warranted, given that findings of villious damage on biopsy is the gold standard of celiac diagnosis.

I'd argue, though, with that Transglutaminase IgA result you really wouldn't need to go through the biopsy, unless it is needed for confirmatory insurance purposes (such as getting subsidies for gluten-free foods).

And yes, low iron/ferritin levels are very much a concomitant sign of possible celiac--your system is likely not absorbing many of the nutrients you take in, bad diet or not.