I'm not exactly following what you're trying to do, but it seems to me that using String.Format would go part way to solve your problem - build a format:
Private sConStrFormat As String = "Provider=TDOLEDB;Data Source=TDDEV;Persist Security Info=True;User ID={0};Password={1};Default Database=bcpm_ddbo;Session Mode=ANSI;"
I would assume that you would be reading your connection string format in from your configuration file (app.config/web.config), so you would define the format in there and then use String.Format to push in the correct username and password.
Then when you want to use it you just do:
Dim UserName As String = "MyUserName"
Dim Password As String = "MyPassword"
sConStr = String.Format(sConStrFormat, UserName, Password)
Using Con As SqlConnection = new SqlConnection(sConStr)
Con.Open
'Do whatever you need with your open connection...
End Using
'....
Does that do what you're looking for? The alternative ConnectionStringBuilder would be more preferable - you just need to overwrite the UserID and Password properties (which are Get/Set), but this is perfectly usable.
Alternatives are to enable integrated security and have the user log into the application and use impersonation or use their windows identity for their interaction with the database. Check out the System.Security.Principal namespace and the WindowsIdentity class for pointers on how to do this.