Variable, really depend on your luck:
1) See when you get your LTA approval (2wks-2mths).
2)After approval, go for medical check-up, I walk in SATA, medical results in a week time.
3)Once medical passed, procced to course centre to book your course, now I think should be able to get one within 2wks. My TDVL was almost a month later, lucky someone dropout, I was offered to stand in a date earlier.
4)After the course, the exam date is usually a week later. The results is immediate,if you happened to fail any of your paper, you can book retake paper immediately, it's on first come first serve basis.
So if everything go smoothly, you can get your VL in 5-6weeks time.
Oh, just some personal suggestions, when applying for LTA approval, tick all options, Bus VL, Bus AL also(so you can also later go for Bus courses: allow you to drive PH 13seater Van) No need to spend another $40 for approval again, and no need to do another medical check-up. Another thing is that go for TDVL better, since it allow your to drive both, more options. And you can use Skillfuture credits for TDVL.