The ASP.NET user is both a user account and a term to identify the user account assigned to the application pool your website uses. You will not find a user named ASP.NET in 2008 R2 unless someone creates it manually and then it will not be a special account anyway (it used to be a default account created when .NET was installed but it hasn't been for a while now). To find out which user account on your machine is assigned to the application pool your site is using, open IIS manager, find your site and select it, click the Basic Settings link in the Actions pane, make note of the application pool name. Now go to Application Pools (it is under the server name directly above the Sites in IIS). Find the application pool with the name you noted and make a note of the Identity. The final step is to make sure the Identity of the App pool has write permissions to the /Data and /App_Data directories.
HTH,
Joe