It is the former. Countries are not allowed to make someone stateless and the UK bill in question explicitly states that this can only be applied to someone with other citizenships available to them. There are different types of birthright citizenship, jus soli (by soil) and jus sanguinis (by blood) where the former depends on where you were born and the latter depends on your parents. The US recognizes both, but jus soli is very much a new world thing while in most of Europe, Asia, and Africa your citizenship depends on the citizenship of your parents. In the case that is the centerpiece of TFA the person being stripped of their citizenship grew up in the UK but her parents were immigrants and she also has Bandladeshi citizenship available to her.
It says available to them, not that they have to have another citizenship or that they can actually obtain one. All the government has to do is declare they're eligible regardless of what the other country says.
For the same reason that, in this case, the UK cannot make someone stateless it is not possible for Bangladesh to do so either. Her Bangladeshi citizenship is by blood and cannot be revoked while her UK citizenship is by naturalization and is therefore relatively easy to remove. This, of course, is discussing things from a rational/legal point of view which is really not the one that is important here; from a perspective of pure power politics the UK is the stronger party in this case so can simply declare a particular reality to be true and there is nothing the others can do about it.
