Why is “bales” the 3rd person singular of “bail”?

TL;DR: Bales is NOT a conjugation of bail; rather, bale is an alternate spelling of some definitions of bail. This was an error introduced by Google's definition-amalgamator. The correct conjugation can be either I/you/we/they bail, he/she/it bails; or I/you/we/they bale, he/she/it bales, depending on the verb intended and your spelling preference (bundling hay is always bale, paying money to temporarily release someone from jail is always bail, but scooping water out of a boat might be either).

Sadly, this is an example of why Google's "definition" results are not quite the same as actually looking something up in a dictionary. These results are amalgamated from various online dictionaries, often Oxford Living Dictionaries (ODO, with whom Google has some sort of agreement) but sometimes other dictionaries, as well. In the process of re-formatting and combining definitions for the results box, sometimes errors or other misleading information can slip in.

In this case, the text at the top of the result does seem to come from ODO, whose entry for bail says in part:

bail¹

^NOUN

1. The temporary release of an accused person awaiting trial, sometimes on condition that a sum of money be lodged to guarantee their appearance in court.
   ‘he has been released on bail’

. . .

bail³

^{(British bale)}

^NOUN

1. [with object] scoop water out of (a ship or boat).
   "‘the first priority is to bail out the boat with buckets’"

   1. 1 Scoop (water) out of a ship or boat.
      ‘I started to use my hands to bail out the water’

2. North American informal [no object] Abandon a commitment, obligation, or activity.
   ‘after 12 years of this, including Sunday Mass with the family, I bailed’

You'll notice that this definition does not specify verb conjugations; it also doesn't include the "let (someone) down" part of the definition. That piece seems to have come from a print book which can be found in Google Books (New Words, Orin Hargraves, ed., 2004) and was published by Oxford University Press but otherwise has no apparent relation to ODO. Moreover, although ODO's bail definition does list bale as an acceptable (British) alternate spelling for some definitions, it also has an entire separate entry for bale where the noun definition "A bundle of paper" etc. can be found (the noun definitions listed under bail are quite different).

So what seems to have happened is that Google's definition-generator has, somehow, mashed-up a variety of definitions from sundry sources—both different entries from the same source and different sources for the same word—and in the process has incorrectly listed bales as the 3rd person present form of the verb bail. A more accurate understanding would be that bails is the 3rd person present form of bail, and bales/bale is an acceptable alternate (primarily British) spelling scheme for some definitions of the word.

As an aside, note that Google "personalizes" all of its search results, so what one person sees is not necessarily what someone else sees when running the exact same search. However, in this case I was able to replicate your result by searching "define:bales" (without quotation marks) and then clicking to expand the boxed definition. Partial screen capture:

But I note that Google returned three entirely different results when searching "define:bale", "define:bails", and "define:bail", none of which showed the same conflation of spellings.

It's a fluke. The page rendering must have got it all mixed up or the image must have been retouched. Google search merely reproduces from the dictionary as it is.

bail³ (ODO)
/beɪl/**
verb verb: bail; 3rd person present: bails; past tense: bailed; past participle: bailed; gerund or present participle: bailing; verb: bale; 3rd person present: bales; past tense: baled; past participle: baled; gerund or present participle: baling
1. scoop water out of (a ship or boat).

Notice the verb: bale; starting in the middle of the paragraph.