Get yourself a full warranty with Warranty direct, at that mileage you will get 3 years complete cover for around Β£1100. Its a far better product than BMW warranty.
I bought my 35i, (same car mechanically) a year ago with 24k on the clock, full history and annual safety checks from BMW.
I purchased as an upgrade from my 23i following advice from my local indy who are excellent.
In my one year of ownership it has cost nearly Β£600 for a DCT sump, gasket, gearbox filters and oil, all paid by warranty direct, (not covered by BMW warranty).
The DCT sump is plastic and WILL warp and leak. You can buy a CNC machined replacement for around Β£1000 but they are thicker and you cannot replace the undertray which leaves the DCT exposed to the elements :thumbsdown:
From my own pocket,
1. Oil/filter change - Β£70ish with labour.
2. Swapped out the adaptive suspension for an eibach kit, a massive improvement in all aspects
3. Swapped out bridgestone run flats for Pilot Sport 4s Β£616 = Β£30 fitting
All the items others mention above are weak spots, water pump is electric and notoriously dodgy as pretty much any mechanic will tell you, HPFP and injectors are the same.
You could buy a 35i for less without the expensive suspension and simply replace the std suspension with eibach for around Β£750!