After a couple of weeks, I think I've finally figured this out. In your project, under build settings, you have a Code Signing Identity set. I currently have all of them set to my iPhone Developer ID, which is included in the Provisioning Profile that I have set (also in Build Settings.) In order to get the Xcode server the ability to use these keys, you need to get them onto the server. Here's what I did:
1) Open up Keychain Access.app on the machine where you created your developer certificate(s)
2) Select My Certificates from Category
3) Right click (Ctrl-click) on your Certificate and Select Export "iPhone Developer:…"…
4) Save the Certificate as a .p12 file (Keychain Access will prompt you for a password to encrypt the file, and for an admin password)
5) Transfer the .p12 file to your Xcode Server
6) Double click on the .p12 file, and import it into the System keychain on the server. Make sure it's the System Keychain and not the login Keychain.
7) Right click on the private key, (You need to click the disclosure triangle, to expose it) and select Get Info.
8) In the Access Control tab, select Allow all applications to access this item and then click on Save Changes.
Viola! Now your Xcode bot will be able to sign your code.
My next tests will include setting my Distribution profile and Certificate, so that the product that the bot creates can be used for distribution in the app store.