Buy / Bought - are these two words allomorphs (of the "past tense" morpheme), or do they represent the phenomenon of suppletion, or perhaps both? Help!
From an etymological perspective, this is not suppletion. The word "bought" is an irregular weak verb: I wrote an post summarizing the history of past-tense forms ending in -ught as an answer to this question here: Origin of irregular ending "-ught" for past simple and participle. The presence of the dental suffix in the past tense caused the root to develop a different form, but it was originally the same root as the present-tense.
From a synchronic perspective, I think it depends on what you mean by "suppletion". There have been arguments about how "irregular" forms like this are mentally stored: some linguists have taken the position that there is a sharp division between irregularly inflected forms (whether or not they are etymologically suppletive) and regularly inflected forms. See e.g. "Whatever happened to the Past Tense Debate", by Steven Pinker (2006). "Bought" is certainly irregular, and so according to the theory that Pinker endorses in that article, modern English speakers would be just as incapable of generating the form "bought" by rule as they are of generating the form "went" by rule. The fact that "bought" starts with the same consonant as "buy" and ends with the same rime as a number of other past-tense forms such as caught, taught etc. would be expected to make it easier for speakers to remember it than if it were something like /dɪmp/. But my understanding is that according to the theory that Pinker describes there, a dichotomy between "suppletive" and "non-suppletive" but irregular forms wouldn't exist as part of the synchronic grammar of English speakers.
I don't know that much about different perspectives on morphology, but according to at least one tradition of morphological analysis, both regular and irregular past-tense verbs can be analyzed as having the same underlying morphological composition: the morpheme of the head verb and the past-tense morpheme. So "bought" could be analyzed as corresponding to the morpheme BUY + the morpheme PAST TENSE. I don't think this is particularly controversial, assuming that you're dealing with an analysis that uses the concept of "morpheme" in the first place (I think people have criticized the concept, but I don't know anything about the alternatives).
I think it's less clear how the two morphemes involved map to the surface form in an irregular word like this. The head verb and the past-tense morpheme could be analyzed as having mutually conditioned irregular surface realizations (e.g. BUY has a special allomorph /bɔː/ used before PAST TENSE, and PAST TENSE is realized as the allomorph /t/ after BUY), or we could just suppose that there is some kind of special rule that replaces this particular combination of morphemes with the unitary (from the point of view of synchronic grammar) surface form /bɔːt/. A term I've seen used to refer to the second interpretation is "portmanteau morph".