Disclaimer: I take no credit for this information, it summarizes what I learned from http://appdb.winehq.org/objectManager.php?sClass=version&iId=15970&iTestingId=44986
Step 1: You need to obtain a legit copy of usp10.dll (found in c:/WINDOWS/System32/ if you have run-of-the-mill windows installation). It is apparently contained in the "Microsoft Installer 2.0" package. Getting it from there is left as an exercise to the reader, especially since I have no idea what the legal implications might or might not be.
Step 2: You need to copy the usp10.dll in the windows/system32 subdirectory of the wine bottle containing your Audiosurf installation.
Step 3: Open the winecfg application for the Audiosurf bottle, go to the applications tab, add the QuestViewer.exe found somewhere below the directory where audiosurf is installed.
Step 4: With the questviewer app selected, change to the libraries tab and add an override for the usp10.dll (so that the native version is tried first).
Step 5: Make the changes to the config file that are listed in tip directly above (fullscreen/autodetect). (This is non-optional as you won't be able to make it go fullscreen from the Audiosurf Menu if you let it start in windowed mode.)
Step 6: Set your dock to auto-hide (optional, but looks nicer since you'll only see the menu bar.)
Step 7: Enjoy.
NB: AAC-encoded files will not work out of the box. See separate hint for installing quicktime into the bottle.