You should be able to use your title company and the bank can use their own. It is called a split settlement and it happens all the time.
It is possible that the bank will refuse to enter into a contract with anyone other than their title company and this could be for a couple of reasons. First, many foreclosures have been undone lately and the bank may want to use a company that they are sure will get the process correct. They don't want to deal with an issue later.
Second, the title in a foreclosure is often messy and it is possible that their title company has cleaned the title and has all the paperwork to show it. If you pick another title company, that work will need to be repeated and it is possible they have trouble fixing all the issues and you don't make it to settlement. The bank does not want to get 99% of the way through the process not to settle.
I would look into a split settlement and if that does not work, I would look into their company if that is what it will take. It may not be the best alternative, but sometimes that is what it takes to get the house. In the end, you will still have a title insurance policy.