Visual Studio is based on sets of functionality in Visual Studio "packages" (vspackages). BIDS is just Visual Studio with the vspackages for SSIS, SSRS, and SSAS development. Those same vspackages can be used through "normal" Visual Studio if you already have that installed.
If you don't have Visual Studio installed, then installing BIDS installs it.
Although you can run SSIS packages outside of VS, there's little you can do to debug them that way. It is not practical to create them outside of VS.
Is there a reason you want to do this?
Yes, you can get rid of VS2005 as far as BIDS is concerned. Install Visual Studio 2008 SP1, then install the SQL Server 2008 bits you need, including BIDS 2008.
If you still need to work with SQL Server 2005 SSIS packages, then you still need VS2005 to work with them.