BD has money to offer and that is all you need. Turkey has nothing to lose by sharing the burden.
Maybe I did not understand what you meant by joining the project.
If BD is willing to put down 2-3 billion US dollars,
then I am sure that BAF can be involved in creating a customized version for BD and getting the planes at the same time as the Turks.
Problem is that this is money that BD would have to put in now and then BD will have to pay more money for the actual planes 10 years down the line when they start rolling off the production line.