Why is borne a past participle of bear?

To be clear, it is not standard to use "bore "as the past participle of bear. Bear has borne as a past participle, and possibly also born, if you consider the "be born" construction to function in present-day English as a passive form of "bear." (To me, the connection between "be born" and "bear" seems more a matter of history, not so much an active connection.)

Many past participles end in -en, -n or -ne. Past participles formed with a suffix containing /n/ are considered irregular today, but they come from the historical conjugation of "strong" verbs, which are a large and important category of Germanic verbs.

Most relevantly, the past participles of tear, wear, swear are torn, worn, sworn. Some other past participles not ending in -ed are done, gone, eaten, broken. There are many more examples. So "borne" is not very exceptional in not using -ed. The fact that it takes the spelling -ne rather than -n (if we leave out the "be born" construction) is more surprising.

All past participle forms, whether formed regularly with -ed or irregularly in some other way, can be ambiguous with adjectives. Many adjectives have the form of past participles: for example, frozen, excited, dejected, disappointed.