Green’s Dictionary of Slang

blue me! excl.

[var. on blow me! excl.1 ]

(Aus.) a general excl. of emphasis.

[Aus] ‘Fanny Flukem’s Ball’ in Bird o’ Freedom (Sydney) in J. Murray Larrikins (1973) 39: I’ll tell you of a ryebuck spree – / Gor’, blue me, it was grand.
[Aus]Truth (Sydney) 14 Jan. 6/6: Blue me you bet your sweet life I’ll stick to it like glue to a basket.