Kristol and other neoconservatives are starting to panic as their boy Jeb tanks in the polls. Christie, Pataki, Graham, and other liberal Republicans aren't going anywhere either.
Fortunately, the strategy of recruiting another liberal Republican to be their standard-bearer will backfire, because it will split the GOP establishment vote, in much the same way that the RNC has been trying to split the conservative vote with a glut of pseudo-conservative candidates.
Bloomberg wouldn't necessarily run as a Republican. More likely: third party or independent.
If all we're talking about is Murdoch tweeting from his yacht on the other side of the planet, maybe Bloomberg won't run at all.