Actually, he does say it comes from his father! From Chapter 63: “これは父さんがエジプトの骨董屋で買って来たものなんだけど…”
Or, loosely: “My dad bought this from an antique store in Egypt…”
Except they DO mention how he got the Millennium ring in the manga. They don’t show it, but I’m pretty sure that Bakura said that his dad got it for him. The explanation is in the chapter right after Yami Yugi duels Pegasus for the first time.
Oh, it was just over here in a completely unrelated chapter. WHOOPS.
YGO Canon Shuffle 
Yep, and if I remember well, we actually saw Ryo’s father in the anime. And I’ve always wondered: is his mom (manga/anime) actually dead like his sister? It was never clear if the two died together…