The Stanford Encyclopedia entry on "Nineteenth Century Geometry" is not quite what you're asking for, but it seems nonetheless likely to be of interest. It's always worth trying this resource for History as well as for Philosophy.
I also found this in Google books, http://books.google.com/books?id=r9C-SCXymPoC&lpg=PA93&ots=LhLRqi5Fkh&dq=geometry%20before%20einstein&pg=PA109#v=onepage&q=geometry%20before%20einstein&f=true, which is considerably closer to an Answer, but still not quite what your Question asks for (you can see in this link that my search term into Google was pretty simple-minded, "geometry before Einstein"). This reference makes it seem as if there was a lot of speculation in the air, perhaps enough that Einstein and others, particularly including Hilbert, would have taken it for granted that geometry was where the story would be, but there's still no sign of the smoking gun.
EDIT: It is perhaps noteworthy that in my pursuit of a more definitive Answer to this Question I find myself stumbling into the substantial literature on one of the great controversies of the last 15 years in the History of Physics, the question of priority for GR, between Hilbert and Einstein. Reading a review of this sometimes acrimonious debate in http://arxiv.org/abs/physics/0504179 (it's a colloquium talk), one is further struck by the extent to which geometry is absolutely in the air for these guys.
EDIT(2): What I think is a better citation (by searching the PhilSci archive): http://philsci-archive.pitt.edu/4377/. The discussion here includes the following, on page 42: "Early in 1914, in a joint paper with Lorentz's former student Adriaan D. Fokker, Einstein reformulated Nordström's theory using Riemannian geometry (Einstein and Fokker 1914)." That it wasn't yet successful Physics doesn't matter, it has already been applied to problems of Physics. Good enough?