After you install SQL Server 2012, the Visual Studio shell is no longer automatically installed. You have to download and install it separately. In addition, starting from Visual Studio 2010, they have changed the BIDS to SQL Server Data Tools (SSDT). There are two versions for VS 2012. SSDT is for the general SQL Server-related application (for VS developers), SSDT-BI is specifically for the BI projects (for SQL Server Developers). The latter is what you need.
Download Microsoft SQL Server Data Tools - Business Intelligence for Visual Studio 2012 here
The x86 version program works fine on the machine with a 64-bit CPU and 64-bit SQL Server 2012. Caveat: When you install it, just choose 'new Installation', not add it as a 'New Feature' to an existing instance.