When I did my CBT, we had some CG125's that had seen better days, even though I'd been riding 125's previously over many years, and was very confident, they where difficult to control and ride smoothly, with such a hiccup'y' power delivery that I hated them with a passion..
When I then had to get on the GS500E for the DAS part (started the same day), I was quite apprehensive, but the bike was 10 times easier to control and just like my mates bikes I'd tried before, very very smooth and controllable.
The thing with the bike is, as long as it's a good bike (and a new CBF125 is), all your fears of 'control' are probably very much exaggerated, the fact you have a healthy fear of your life, and are concious of the control aspect, I'd say that you are probably in the right place, and will go very slowly to start with, exactly what people need to do, as you saw, everyone else there had similar control to your self (that's what it sounds like from your description), and I'm sure at your own pace this will translate to safe riding..