Allecto, one of the Furies, is commonly associated with dark colours and snakes (see Pauly–Wissowa on the Furies). Furies often have snake hair too, and snakes are often blue; they don't look like ordinary women. So Allecto took a snake from her dark-blue snake hair.
Caerulus can mean "dark" as an epithet to words like death and rain, but Lewis & Short connect it with snakes and the Furies under the sub-sense "of other darkblue objects", in a quotation from Virgil's Georgics:
Quin ipsae stupuere domus atque intima Leti
tartara caeruleosque implexae crinibus angues
Eumenides, tenuitque inhians tria Cerberus ora
— Virgil, Georgics 4.481–483.
Even the Eumenids (a common euphemism for the Furies) themselves are stupefied as Orpheus enters the underworld. They are entwined with caeruleae snakes in their hair.
Ennius mentions a caerulea anguis in his lost play about Alcmaeon. Cicero quotes Ennius's play when discussing madness, in which Alcmaeon is attacked or oppressed by the Furies:
'Fer mi auxilium, pestem abige a me, flammiferam
hanc vim, quae me excruciat!
Caerulea incinctae angui incedunt, circumstant
cum ardentibus taedis.'
— Ennius, Alcmeo (lost), in: Cicero, Academicae Quaestiones 2.28.
The Furies are coming towards him, surrounded with a caerulea snake. So this is an old collocation. Presumably snakes surround the Furies' heads, and even their entire bodies. I, too, am often seen with snakes all over my body, and they and I are all associated with Tartarus.
Ovid, too, describes the hair of the Furies as containing or consisting of serpents:
obstitit infelix aditumque obsedit Erinys,
nexaque vipereis distendens bracchia nodis
caesariem excussit. Motae sonuere colubrae,
parsque iacent umeris, pars circum pectora lapsae
sibila dant saniemque vomunt linguisque coruscant.
Inde duos mediis abrumpit crinibus angues
pestiferaque manu raptos inmisit. At illi
— Ovid, Metamorphoses 4.490–496.
Here you will see a few pictures of the Erinyes and an old selfie I had lying around (from Greek vases, 6th to 3rd centuries BC):
— Orestes at Delphi flanked by Athena and Pylades among the Erinyes and priestesses of the oracle, perhaps including Pythia behind the tripod - Paestan red-figured bell-krater, c. 330 BC.
— Erinyes, Apulian red figure krater C4th B.C., Badishes Landesmuseum, Karlsruhe.
— Collection: TBA (Taranto?), Laconian Black Figure, Kylix, C6th BC: Kerberos, the three-headed guard dog of Haides, is depicted draped in a mane of snakes. The bird flying above him probably represents a flittering soul. Herakles enters the scene on the right with only his club and foot showing.