[Marcello]

"Thing is, I can't find data on bomb bay layout in the Tu-160 (or earlier Tupolev bombers btw), so I don't know how many of which bombs you can fit in."

I do not have much time at the moment, so you will have to wait for further details and sources. But as far as I remember the only weapons that can be carried in the standard version are Kh-55/Kh-15. No conventional bombs or stuff like that. The modernization which is being carried out should enable enable various conventional bombs to be fitted.
But the non modernized planes are specialized missile carriers with no free fall bombs capabilities.