Online Etymology Dictionary
dive emerged 13c. from O.E. dufan "to dive, duck, sink" (intransitive, class II strong verb; past tense deaf, pp. dofen) and dyfan "to dip, submerge" (weak, transitive), from P.Gmc. *dubijanan. Past tense dove is a later formation, perhaps on analogy of drive/drove. Sense of "disreputable bar" is first recorded Amer.Eng. 1871, perhaps because they were usually in basements, and going into one was both a literal and fig. "diving."
It seems that folk irregularisation is similar to an older irregular form, if I deaf can be counted as similar to a modern I dove. Auferre, trucidare, rapere, falsis nominibus imperium; atque, ubi solitudinem faciunt, pacem appellant.
But with "dive", the strong form's past tense is deaf (pronounced with two distinct vowel sounds, something like dé-af), which is unlikely to have survived as "dove". The analogy with "drove" is the most probable explanation. When locusts move on, they leave nothing behind
