I meant to post in here when I saw it last week but forgot, so I'll say my piece now

I was in a similar situation about 18months/2 years ago (I was 21 at the time), I'd always wanted to ride but never really had the inclination to do anything about it, bit of a pipe dream if I'm honest. I mentioned it to my GF's dad (Shooey), who suggested I donned a set of his spare leathers and went out on the back of his bike with him. I agreed, and off we went.
I really enjoyed myself and he said if I promised to take my test/get a bike, that he'd let me have his spare leathers cheap. I'd long passed my driving test (3 yrs) and been driving for some time, and before that I'd always ridden a push bike and would regularly go for longish rides so I had a fairly good road sense.
I weighed everything up and went and did my CBT/theory and decided it would be best to just crack on and do my DAS all at the same time, which I did. Since then I've bought a CBR600f and really enjoy riding it, and I'm definitely glad I didn't get a 125 in between as I wouldn't have had the funds to get the CBR.
So, my tuppence would be to just get on with your DAS! As I've said, my only road experience on two wheels before my CBT was on a push bike, and I managed just fine! At the end of the day, a 600 is only a heavier 125! If you don't twist the throttle wide open it'll do exactly the same speeds as a 125, but the upside is it gives much more room for future growth. At the end of the day, you're not a young lad who thinks that they're invincible (judging from the fact you say you've got 20 years driving exp), so yeah, go for it!
EDIT: Forgot to mention, most training centres have 125's that you can rent for a reasonable rate. Might be worth grabbing one for a few sessions to get that little extra experience. I didn't but did do the full 3 day DAS course (and failed my first time, put my foot down

)