I've got a high mount rack from my old car (with the dumbell things), but I've been told Honda do not advise you use them on the civic. Civinfo threads pretty much say the same and a number of the websites selling racks show compatibility and the Civic is shown as incompatible.
The stress on the glass and the spoiler is one thing and also the straps would be difficult to thread up past the rubber seal. Not sure where the bottom straps would mount to either.
At the moment the bike just goes in the back of the car with a sheet (front wheel off). Still means the car gets dirty. I might look into a bike bag.
Don't really want a roof rack. Don't want the hassle of removing/fitting the rack all the time or leaving it on and having wind noise when driving, plus down country lanes the bike can clip overhanging trees.
Other option is a tow bar fitting. I don't have a tow bar and don't really want one, but it's an option I may look into. Though having the bike in the boot is handy for just keeping it in there ready for jumping out for a ride whenever I want.