The other option available is to 'pin' the bridge so that it is kept in the right place for the strings, but it does mean that the strings will then run at a slight angle back to the tailpiece. Pinning the bridge is something you may want to do anyway later if you find the bridge slips around in use. Best done once you've set up the guitar and got the position right for best intonation with your choice of strings, so that you can mark the correct position with tape before fixing it.

You can also use double-sided tape rather than pinning, but I'd prefer direct bridge-to-top contact rather than put a softer layer in-between the two that could affect vibration transfer. But it is something you can easily try and then remove if you don't like it. But the tape glue could affect some kinds of finishes (though it will obviously be hidden by the bridge).