What do you have target platform set to in the project?
VS2008, by default, usually sets it AnyCPU, which means it will run as 32 bit on a 32 bit OS, and 64 bit on a 64 bit OS. However, if you set it to x86, then it will always run as 32 bit, and as such require a 32 bit client install. VS2010 on the other hand, defaults to x86
Are you running this in the development webserver that comes with VS? Or IIS? If I recall correctly, the webserver built into vs2008 is 32 bit, so that's probably what's happening. If that's the case, then yes you'll need to also install 32 bit client. If you deploy it to 64 bit IIS (and have not enabled "enable 32 bit applications" for the app pool), then you'd need a 64 bit client.
Hope it helps,