My apologies for not responding sooner.
I wanted to not just rely on my books but ask this question to Old Believers much more competent than I ever could be. One whom I corresponded with was born into an Old Believer family in Oregon, belonging to Belokrinitsky, "priested Old Believers" , and has been an Old Believer all his life, has been the most helpful. Old Believers do not feel bows and prostrations to be strictly divided in the sense that a prostration is worship and a bow is veneration. - This does not mean other Orthodox believe this but I have encountered this misconception amongst Orthodox about the meaning of bows and prostrations - They understand bows and prostrations in the context of Tradition, of the whole cycle of prayers within the cycle of Church Services within the whole cycle of the Church Calendar. The only prayer to the Theotokos where a prostration is always made no matter what day or time of year is the "Axion Estin" AKA "Dostoinno est" AKA "It is Meet and Right . . . " This is a practice of veneration that has been handed down through Tradition and is simply accepted as such by Old Believers. There are many prayers to the Theotokos when a prostration is not prescribed and there are many more times when prostrations are made when it is not a prayer to the Theotokos.
Would anyone happen to know why bows/prostrations according to the Old Rite seem to accompany prayers to the Theotokos more frequently than those to the Holy Trinity?
This is simply as you put it: something that seems to be the case but really when you delve deeper is not. Factually this is not true . Throughout Lent prostrations are prescribed more often than during the rest of the year at several places during all Church Services when a bow would be the norm otherwise and are most often prayers to the Holy Trinity or Christ. On weekdays the Entrance Bows and Departure bows are prescribed to be to the ground AKA a prostration AKA "Zemkoy Poklon". Prostrations as part of a private rule of prayer are encouraged and most often accompany the Isusova molitva AKA Jesus Prayer.
I don't know why but it seems odd to me.
Encountering the "old-fashioned" or "old world" piety often is seen as odd by most Orthodox raised in Modern culture. The act of venerating icons by making prostrations is the prescribed manner on weekdays but is seldom followed in my experience. Even the act of making a prostration on Great Friday is not followed by many Orthodox when they attend Great Friday services. But I don't know if this is your meaning or it is something else?
When I was a kid I was only exposed to Roman Catholic piety. When I first saw the way Muslims pray making a prostation I remember thinking that I wanted to pray like that. It was only years later tha I learned this form of prayer was adopted from Orthodox Christianity. It seems very natural and pious to me and though at first I tended to feel that a prostration should be "limited" to worshipping God but I realized that veneration of the Mother of God and Saints & Angels is worshipping God!
Separately I would just like to add that pious devotion to the Mother of God is something that I've encountered over and over again when reading about and encountering Orthodox people from Orthodox cultures as they exist in rural areas influenced by monasticism, that is, the monasteries in the area the lay people inhabit. Elder Paisie (Olaru) and Elder Cleopa (Ilie) counseled lay people to pray the Akathist to the Mother of God in the Morning and her Canon at night, her canon is normally read as part of the Compline service, and Elder Paisie additionally encouraged praying personal prayers to her begging her love, mercy, forgiveness and help calling her "Sweet Mother!"
The Old Rite just confuses me.
I can't keep up. Lenexa seems to have a love for all things Old Believer, so perhaps he can bring you up to pace?
What is confusing about it for you? Is it the Old Rite itself or the Old Believer culture that is confusing?
I would recommend that for those who want to have a better understanding of why we, I mean all practicing the "Byzantine Rite", pray what we do, how we do, and when we do the book Treatise on Prayer
by St.Symeon of Thessalonikehttps://securehost85.hrwebservices.net/~cotn//shopping/product_info.php?cPath=21_23&products_id=457&osCsid=9b71b1aab4afcf6b0194f6ab4dda1f27
Hope this helped!
Please pray for this sinner, his family and pray for all who passed on this info to me!