The earliest use of 'bloodbath' I could find was a 2 March 1795 hyphenated use, referring to the French Revolution, in the Caledonia Mercury (Midlothian, Scotland; paywalled):
Legendre — ".... Never shall the spirit of Terror and the reign of Blood be revived. Go take the blood-bath with cannibals. The National Convention of France has decided that you shall cut throats no more...."
An apparent earlier use in a 1752 edition of Shakespeare's "The Life and Death of King John" (Act II, "Blood bath bought blood, and blows have answer'd blows; // Strength match'd with strength, and power confronted power.") is an editorial or printer's error.
The compound, as suggested by the OED, formed within English, rather than being adopted from comparable Dutch, German, Swedish or Danish compounds. Those similar compounds, although characterizable with more nuanced meaning ("a massacre", "a battle"), had in 1795 been extant since at least the 15th century. As a matter of speculation, however, knowledge of those compounds may have sponsored the use by Legendre (a butcher from Paris) at the French National Convention on 15 February 1795.
The earliest attestation shown by OED, is found in the 1814 publication of Illustrations of Northern Antiquities, from the Earlier Teutonic and Scandinavian Romances, wherein the Scottish dialect 'bluid-bath' is glossed with English as 'blood-bath' and both ('bluid-bath' and 'blood-bath') are noted to be translations from Danish for "a battle":
Bluid-bath, blood-bath; a Danish denomination for a battle.
The appearance in the R. Jamieson translation of "Stark Tiderich and Olger Danske" is only one of the three appearances in Northern Antiquities. Other appearances include the gloss already mentioned and another from the Danish romantic ballad "Oluf Pant" (from the Danish Kæmpe Viser, also translated by R. Jamieson; emphasis mine):
I' the hen-bauks up Oluf Pant he crap;
There he was nagate fain;
The Prior took tent whareas he sat,
And in blood-bath laid him then.
The next use of 'blood-bath' I could find was in Thomas Carlyle's 1832 essay, "Boswell's Life of Johnson", and again refers to the (then historical) French Revolution:
The strongest man can but retard the current partially and for a short hour. Yet even in such shortest retardation may not an inestimable value lie? If England has escaped the blood-bath of a French Revolution; and may yet, in virtue of this delay and of the experience it has given, work out her deliverance calmly into a new Era, let Samuel Johnson, beyond all contemporary or succeeding men, have the praise for it.