You need Picatinny rings to fit to the Picatinny rail that you have installed on your Begara, the bases that fit a standard Tikka dovetail are entirely different and are not compatible with the Picatinny system.
If you already have the Optilock system on your Tikka you could simply replace the standard Tikka/Optilock dovetail bases with Picatinny style Optilock bases and utilise your existing rings.
Alternatively and probably cheaper would be to simply purchase a new set of Picatinny rings of the correct tube diameter and height and install these on your Picatinny rail. The available range of Picatinny rings available is massive as is the quality and price range.
You don't seem to have spared the cash by installing a Tier One rail, so why not consider a set of Tier One rings to go with it.