I've tried googling for this, but haven't been able to come up with a definitive answer. How do I cite in a footnote in Bluebook format a contract between party A and party B signed in 2008?
The point of the Bluebook is to give uniform citation rules, so that anyone who reads a citation to a public record like a case, statute or regulation will be able to find it for themselves. It's generally used for brief writing.
If you're talking about a private contract between two individuals, nobody is going to be able to look it up, because it's not a public record; there is no "citation" that will magically get them to it.
Instead, you would ordinarily attach the contract as an exhibit, then cite it accordingly. On first reference:
April 20, 2014 Agreement of Sale ("Sale Agreeent"), attached as Exhibit A.
On later reference:
Sale Agreement (Exhibit A).
Of course, your court's citation rules may vary.
If you're looking to cite something for an academic paper rather than a court filing, and you have to use bluebook format rather than a real academic citation format like MLA or Chicago, follow rule 17.1, the general rule for unpublished materials. For these purposes, a contract is no different from a letter or another non-public document.