$PSBoundParameters isn't what you're looking for. The use of the [CmdletBinding()] attribute allows the usage of $PSCmdlet within your script, in addition to providing a Verbose flag. It is in fact this same Verbose that you're supposed to use. 
Through [CmdletBinding()], you can access the bound parameters through $PSCmdlet.MyInvocation.BoundParameters. Here's a function that uses CmdletBinding and simply enters a nested prompt immediately in order examine the variables available inside the function scope.
PS D:\> function hi { [CmdletBinding()]param([string] $Salutation) $host.EnterNestedPrompt() }; hi -Salutation Yo -Verbose
PS D:\>>> $PSBoundParameters
____________________________________________________________________________________________________
PS D:\>>> $PSCmdlet.MyInvocation.BoundParameters
Key Value                                                                                                                                                                                                           
--- -----                                                                                                                                                                                                           
Salutation Yo                                                                                                                                                                                                              
Verbose   True                                                                                       
So in your example, you would want the following:
function DoStuff `
{
    [CmdletBinding()]
    param ()
    process
    {
      new-item Test -type Directory `
        -Verbose:($PSCmdlet.MyInvocation.BoundParameters["Verbose"].IsPresent -eq $true)
    }
}
This covers -Verbose, -Verbose:$false, -Verbose:$true, and the case where the switch is not present at all.