That having been said... (thanks for being the wise eye, ND
The tiptronic should never
be used for racing purposes; pretty much for economy or towing. The thing takes a VERY long time between shifts... A blind person without any hands is faster. The sport mode, although not allowing you to shift at your own desire, is much faster than the tiptronic could ever be.
If you prefer the tiptronic anyway, you'll find that at full throttle you'll want to shift about 800-1200 rpms before the point you want the car to shift. It's that slow.
I suggest that you keep it easy; if you want to learn to drive fast safely
in an automatic, you'll need to learn your car. I mean that in much more of a way than if you are driving a manual: if you are driving a manual, you're pretty much telling your car what to do. If you are driving an automatic, you're asking it to do something for you.
Test out your car's shift points at different pedal pressures. With enough experience (and the kickdown function is very helpful with this) you'll find out that it is possible, albeit complicated, to force your car into upshifts or downshifts (much easier, with kickdown, to instigate a downshift) or hold gears at high revs/low revs (again, easier to hold in low revs due to the nature of the automatic) without ever
going out of S or A/E mode. And it's much quicker that way, for the car, than if you did tiptronic.
E.g., I know in my 318i, pressing kickdown in any gear will drop a gear; hold at about 1/4 pressure on the accelerator, and the car will hold the lower gear at about 5500 rpms (while maintaining constant speed) for around 5-7 seconds. Feathering the throttle with more pressure can extend that to up to 10 seconds. It's all about deluding the car into what you want it to do. Make it think you are going to use those extra revs, or conversely, make it think you are going to go faster, so that it jumps up a gear, and then make a good 40mpg economy at 1200rpms whilst going 45-55mph (by holding about 1/8th pressure on the accelerator after pushing down 3/4's to instigate a gear change).
Complicated with an auto, but with experience, you'll get it.
Or you can always just get a clutch and get manual, or be all tech-savvy and get an SMG.