When you are entering a new booking, you don't need to compare every booking
against every other one - just the proposed booking against the others.

You can do that with a DLookup() in the BeforeUpdate event of the form.
Something like this:

Private Sub Form_BeforeUpdate(Cancel As Integer)
   Dim strWhere As String
   Dim varResult As Variant
   Const strcJetDateTime = "\#mm\/dd\/yyyy hh\:nn\:ss\#"

   If IsNull(Me.BookingStart) Or IsNull(Me.BookingEnd) Or IsNull(Me.RoomID)
Or _
       ((Me.BookingStart = Me.BookingStart.OldValue) And _
       (Me.BookingEnd = Me.BookingEnd.OldValue) And _
       (Me.RoomID = Me.RoomID.OldValue)) Then
       'Ignore cases where there was no change, or values are missing.
   Else
       strWhere = "([BookingEnd] < " Format(Me.BookingStart,
strcJetDateTime) & _
           ") AND " & Format(Me.BookingEnd, strcJetDateTime) & _
           " < [BookingEnd]) AND ([RoomID] = " & Me.RoomID & _
           ") AND (BookingID <> " & Me.BookingID & ")"
       varResult = DLookup("BookingID", "BookingsTable", strWhere)
       If Not IsNull(varResult) Then
           If MsgBox("Clashes with booking number " & varResult & vbCrLf &
_
               "Continue anyway?", vbYesNo + vbDefaultButton2) = vbNo Then
               Cancel = True
               'Me.Undo
           End If
       End If
   End If
End Sub