I managed, but it wasn't easy. Even then, I still get an error, so, while I'll post my method, I would like it if someone had a perfect solution.
Peter's method:
Start with a bottle. Mine was an XP bottle.
Go to www.rockstargames.com/classics/gta.html and download Grand Theft Auto (they made it available for free).
Unzip the resulting file, GTAINSTALLER. The result is a .exe installer and a ReadMe.
Go to ~/Library/Application Support/Crossover Games/Bottles/ (the "~" tilde means your Home folder on the computer).
Inside this folder, pick your bottle of choice (if you have more than one), then go to drive_c, and Program Files.
Next, drag the GTAINSTALLER folder (or just the .exe file) to Program Files.
Open the .exe file in Crossover Games, and let it do the work for you. Crossover Games will ask you to extract the file to a temporary folder (TEMP), and once that is done, the GTA installation process begins. Follow all on-screen instructions.
Now, GTA is installed on your bottle.
If you launch it now (the "Grand Theft Auto.exe" contained in the WINO folder inside the main GTA folder - make sure you open it with Crossover Games [haven't tested with Crossover "normal"]), you can play without a problem.
!!HOWEVER!! this will cause a problem later on: the second time you launch the game, you won't be able to play.
My workaround for this has been to change the permissions for the file "REPLAY.REP", found inside the GTADATA folder. To do so, select the file and hit "Cmd" + "I" ("Get Info"). In the lowest panel, "Sharing & Permissions", change all permissions to "Read only".
With this fix, you can play.
One problem, however: once you quit a game or finish a city, you'll see an error appear. Your player will therefore not be able to ever save his/her progress within the game, and you won't see the end-city cutscenes.
Because of this, you can't unlock other stages of the game unless you use the "itsgallus" cheat.