I am not a Maths expert but have DC who took FM and were interested in Maths at uni (though did not follow that path). When they investigated, universities below the very top tier typically had a round 50% of entrants who had taken FM, so those without FM or possibly grades below A in FM were accommodated by the pace set in the first year at university. There is lots of choice, which is great.
Perhaps a discussion with school or college about why they are predicting a B in FM would be helpful? If they feel, for example, with good logic, that pure maths is not/is unlikely to be your DD's forte, that indicates courses with a high pure maths content and/or cohort displaying confidence in pure maths are courses to be wary of. Equally, it might be that the EPQ was a time sink in Y12 and Y13 may prove to be a period when practice time increases and confidence grows, and so competitive entry courses may actually be perfectly sensible options, but you would need to ensure registration deadlines for any relevant tests have not been missed.
U of Bath does offer on a grade B at FM for their BSc Maths, Stats and Data Science course; this is because they are looking for strong interest in statistics and recognise that strong grades in FM typically need strong performance in core pure maths, which is not everyone's cup of tea. However, you do need to hit Astar in Maths, and you will need to demonstrate stats and data science are areas of genuine interest, and there are pure maths modules to pass whether you like it or not. This leads me on to say that you can have exposure to maths and 'dilute' it in 'Maths &' or Maths with' courses.
It would be unusual to attempt to sit TMUA, MAT and STEP and each, ideally, require their own pre-test practice. The TMUA has undergone recent re-jigging (so check the TMUA website for latest position); I think your DD will have already missed the registration deadline for the first wave of TMUA but (I think and without cross-checking) be able to register for the January test. However, the result from that test will not be available until after the prior consideration deadline in late January and so could not be used to decide on the five UCAS choices. Sitting the TMUA will, however, give a pre-A level sense of where they sit within the top end of the potential maths cohort. My DC used it is that way to finesse choices.