There's no universally correct answer to this one. It depends on terrain (level or not), surface (how lumpy / made of what), etc.That said, I personally much prefer the 'mat inside bivvy' option when it's viable as everything stays in place better. It will also depend how big your bivvy bag is and how thick the mat is. I used a Thermarest Neoair Xtherm (about 6cm thick, but mummy shaped, inside a mummy shaped bivvy with a mummy shaped sleeping bag, which is great if you like the feeling of being very enclosed and with not a lot of room to move (well, none really!).
The big upside is neatness and speed: you can keep everything in the bivvy bag all the time and just unroll it, which is excellent and avoids any risk of anything being wet other than the outside of the bivvy. Stops you rolling off the mat, or sliding off it down a hill, too :-)