It is probably because "bit" is used very colloquially (or in some dialects) as the p.p. of "to bite". I don't know for sure, but I suspect the earlier forms of p.p were also "bitten", as the -en ending generally occurs in more ancient forms of the language (e.g. "to get" with p.p. of "gotten" in former times (and America, of course)).
Bit is still acceptable as the past participle in AE, but is normally limited to set phrases.
The verb has a past tense, bit, and two past participles, bitten and bit. Bitten is much more frequently used in Standard English, but bit continues to occur as past participle, especially in idioms such as these: The other cowboy had already bit the dust. We have bit the bullet. He’s been bit by mosquitoes. All these are Standard, although Edited English would more often use bitten in other than these idiomatic instances. Predicate adjectives such as snake-bit and dog-bit are Substandard and dialectal.