Sudden thought:
It's possible that she's not after marriage. It's possible that, instead, she's only after a spot as a concubine.
Why?
Because if she was a concubine instead of a legal wife, then her children will bear her family name instead of Bell's. Which means that her children would be able to borrow a bit of their father's (Bell's) power and influence to rebuild their mother's (Katharina's) fallen house.
It'd be a brilliant stroke on her part. She could still be considered as being part of Bell's household this way - being a concubine doesn't mean that it's mandated that you be a pillow woman and nothing more. In Frank Herbert's Dune, Jessica, the mother of the main character, Paul Atreides, was actually a concubine and not Duke Leto's legal wife.
In other words, even as a concubine, Katharina can still play a pivotal role in Bell's house as their political "fixer", earning her own merits, and cashing in on those merits to rebuild her house through the children she has with Bell.