Put a hash at the end of the constant, and declare it as a 'double'...
I did this with my bitmask fields:
Public Const EDIT_TRANSACTION As Double = 1073741824
Public Const EDIT_DWRDELIVERY As Double = 2147483648#
Public Const ENTER_DWRORDER As Double = 4294967296#
Public Const DELETE_DWRORDER As Double = 8589934592#
Public Const DELETE_TRANSACTION As Double = 17179869184#
Public Const DELETE_WATERORDER As Double = 34359738368#
Public Const ENTER_METERREADING As Double = 68719476736#
** EDIT **
I guess I got marked down on this because this was old code I wrote for VB6, and not exactly what you were asking for. So, if anyone reading this is using VB6, and have to pass Bitmask fields to something like SQL, this is what worked perfectly for me.
Otherwise, just keep voting my answer down. :)