The short version is, for the purposes of etymology, "bail" is preferred and "bale" is considered an error. There is a word "bale" but it has quite a different meaning.
(It is worth noting that in “The vessel was holed beneath the waterline and the crew bailed [out].” It is not possible to say if the crew jumped over the side or they tried to remove the water.)
The OED, in an entry that has not been as yet fully updated since 1895 gives:
Etymology: Erroneous spelling of **bail v.4
To lade or throw water out of a boat or ship with buckets (formerly called bails) or other vessels. Const. to bale the water out, bale the boat (out). to bale up: to scoop up. See bail v.4
1842 F. Marryat Percival Keene I. xvi. 231 Let's bale the boat out first.
Etymology: < bail n.5 Now often less correctly bale v.3 To lade or throw water out of a boat, etc., with buckets (formerly called
bails), pails, basins, or other vessels.
a. To bail the water (out).
1829 F. Marryat Naval Officer II. i. 14 One [man] to bail the water out.
You will note that both examples are from the same writer. The confusion deepens with the earliest mention:
1627 J. Smith Sea Gram. vi. 27 To baile or cast out the water.
This leads to:
1. to bail out.
a. intransitive. Originally U.S. Of a person: to make an emergency descent by parachute from an aeroplane.
1925 Oakland (Calif.) Tribune 1 Sept. 2 b/3 The..pilot who has to
‘bail out’ hurriedly from a crippled or burning plane.
1939 F. D. Tredrey Pilot's Summer 28 If you bale out and land
in water..a smart rap will release the whole lot and you can swim
And the extended sense of
b. intransitive. colloquial. To leave hurriedly; to escape an unpleasant situation or abandon a burdensome responsibility. Also with
of or on.
1941 R. Riskin Meet John Doe in Six Screenplays (1997) 623 Boy
Midget. Come on, Snooks—you better bail out. Girl Midget. Goodbye, Mr.
c. intransitive. Originally and chiefly Surfing. To jump or dive off a surfboard in order to avoid injury when a fall seems imminent; to
make a similar jump from a bicycle, skateboard, etc.
1962 T. Masters Surfing made Easy 64 Bailing out, getting off
and away from the surfboard on purpose.
a1970 S. Afr. Surfer 1 ii. 27 in Stud. in Eng. (Univ. Cape Town)
(1970) 1 32 Some kook dropped in on my best wave. He pearled as I
came through a hot section. I had to bale out.
And finally we arrive at bail in the sense of to leave rather than stay; to desert; forsake [someone/something].
2. slang (originally North American).
a. intransitive. = sense 1b. Also with on.
1977 G. F. R. Filosa Surfer's Almanac 181 Bail,..to leave,
1982 M. Pond Valley Girl's Guide to Life 51 When you skip
school.., it's cool to go, ‘like, I bailed, man.’ Or when you leave a
party, you go, ‘Let's bail.’