Ryan his son were the only ones who could use the bathyspheres, but I think Elizabeth and her powers didn't have a problem with that.
Here's a possible theory on Dewitt being able to use the Bathyspheres in rapture. All of the dates, ages, and information I am using comes from the Bioshock wiki (LINK
/). I'll include a TLDR version at the bottom:
Just to give some quick background information for those who don't know, only Andrew Ryan or someone with his genetic code are able to use the bathyspheres in rapture. Dewitt uses the bathysphere in Rapture in the end of Infinite.
The lutece "twins", Robert and Rosalind, weren't actually twins. They were just a male and female version of the same person from different "timelines".
Now, using that same concept, apply it to Anna and Andrew Ryan. What if Anna and Andrew Ryan are a girl and boy version of the same person, or possibly a girl and a boy Dewitt had from 2 different mothers in 2 different dimensions. Yes, I know Ryan is from Russia, but it's possible that Dewitt and a woman from Russia had a baby together in one dimension.
In this scenario Dewitt would be the father of Andrew Ryan which explains why Dewitt can use the bathyspheres (similar genetic code). The timelines seem like they match up too, Dewitt was born in 1874 and was 38 when he arrived in Columbia in 1912. Elizabeth was born in 1892 making her 20 in 1912. Now if we assume Ryan was born at the same time as Elizabeth, and he arrived in Rapture in 1946, that would make him 54 years old when he founded Rapture, and he was killed by Jack in 1960 he was 68 years old, not unrealistic at all.
TL;DR: Booker Dewitt is the father of Andrew Ryan in one or more dimensions which explains why Booker can use bathyspheres in Rapture. Andrew Ryan is possibly a male version of Anna Dewitt much the same way that the Letuce "twins" are a male and female version of the same person.
This post was edited on 4/4 at 4:49 am