We do something like this. It is not 100% clear but it looks like you want to do the build and deployment as two separate builds in TeamCity with an artifact dependency from the deployment build on the main build which is exactly what we do. Here is how we do it.
Setup your artifacts from the main build which it sounds like you have already done.
Example: **\bin\release\*.* => bin
Set up the artifact dependency (we also do a snap shot dependency as well but you don't have to) to pull your artifacts from the main build and put them into a local folder in your deployment build.
Example: Artifacts paths: bin\**\*.* Destination path: bin\
We use a mixture of MSBuild and PowerShell for doing the actual deployment work. In each case you can reference the artifacts using a relative path.
IF the build work folder looks like this:
root
|- bin (Artifacts pulled in from main build)
|- src
|- build (Where your build and deployment scripts live)
You would access the bin files from your deployment script located in the build folder like:
..\bin\[your files]
You can then pass the path to your build artifacts like this
%teamcity.build.checkoutDir%\bin\