Well first off welcome to the forum. :lol:
As others have already said swapping to non-runflat tyres should make a big difference.
If the ride still feels very firm it would be worth checking what suspension you have. Facelift models (2006 onwards) came with SE or Sport designations and the Sport ones had M-Sport suspension which was 15mm lower and stiffer.
I think the M-Sport set-up was an option on earlier E85s, so you'd need to do a spec check using your VIN to see what your car had orignally.
Having said that by now quite a few Z4s have had lowering springs, typically Eibach or H & R, fitted as well as uprated dampers like Bilstein.
And we do like to see a photo or two of new members' cars!