I don't think this question has a simple answer. I checked the death index for pre-1850 Cincinnati, and there is no Stegemann matching Maria Elisabeth or Gottfried. If they had died in Cincinnati, they should have showed up.
There was a Bernard H. Stegemann who came through New Orleans 28 Oct 1846 (age 35) going to Cincinnati with wife Elisabeth (age 25) and son Gottfried (age 1). This matches your immigration record.
There was also a Bernhard Stegemann who came through New Orleans 10 Nov 1849 (age 38) going to Cincinnati (he was born in Dinklage, but his last residence was Cincinnati) with children Lisette (age 14), Heinrich (age 11), Dina (age 8) (all children's last residence was Dinklage), and maidservant Catharina Brünings (age 24) from Lohne (listed right after Dina). There were also two Meyer maidservant women from Lohne (Margaretha, 30 and Catharina, 24) in the list right after Catharina Brunings, and a Heinrich Bröring (age 20) born in Lohne, but last living in Bakum further down the list.
Bernd marries Catharina (presumably the maidservant) almost as soon as they get home on 1 Dec 1849 (it would have taken a while to get from New Orleans to Cincinnati back then). In the 1850 Cincinnati Census you find Bernhard (age 36), Catherine (age 25), Elizabeth (age 15), Henry (age 12), and Bernairde (age 9).
I think the dad (and mom/son?) went back to get some kids from his first marriage and maybe mom and son died somewhere along the way (or maybe in Germany, but I did a quick search and didn't find the mom's death in Dinklage or Lohne records online on fak-om). An alternative is maybe they lived in Kentucky and Bernd went back to get the older kids after wife and son died on this side of the River (they would not show up in Cincinnati death indexes if they died over here).
You say below that Maria Elisabeth Stegemann nee Willenborg was Bernd's second wife. Did he have children matching those above with the first wife? Do you have any immigration records in Germany for people coming from the US to Germany? I tried to find Bernd (and maybe wife and son) going back to Germany but had no luck.
If you want images of the census and ship records, let me know and I can send them offlist.