That's the usual Catch 22. The bank wants to see you're enrolled, but you can't do that without the money to apply in the first place.
The professional studies loan is normally given to university professionals such as medical or law students. In those cases, you need to get a place on a competitive course but there is no cost involved in applying. In our pilot world, you can sign up to most schools by giving them some cash. There is no formal application process although some schools (particularly the 'big three' integrated ones) like you to fill in forms nonetheless.
The solution is to ask the school to write a letter saying they'd be willing to offer you a place if you had the money for the deposit. I ended up simply explaining to the bank that a 'proof of acceptance' onto a course doesn't really mean much for flying training as it might do for applying for a Masters course. The bank seemed happy with that explanation.
Otherwise, if you're going modular, you're faced with having lots of 'proof of acceptance' letters from your groundschool, your CPL/IR school then perhaps your MCC school. This is all nonsensical since, if you're like me and you've just started groundschool, you probably have an idea of where you want to fly but it's not yet definite.
Hope this helps!
Ratpup