Look into the bus schedule to see if you can:
Park at Hvolsvollur, jump on a bus to Skogar
Do your hike, catch the Thorsmork->Reykjavik bus, jump off at Hvolsvollur
This is what many do during the summer season, it should still be feasible in September. The fares are a bit lop-sided, with the short stretches to/from Hvolsvollur priced higher than the distance would warrant - but that's only to be expected :-)
Instead of Hvolsvollur you could leave your car at Seljalandsfoss (or the parking lot right at the intersection of the ring road and the road to Thorsmork) - but there would be an increased chance of vandalism and you might not be saving any money on fares (though you can check). I would think that flagging down an eastbound bus at the parking lot should be feasible even if it isn't an official stop (jumping off the Thorsmork bus certainly would be) - but that's another thing you might want to ask about.
BTW, since you mention the Strætó schedule - do check out www.BSI.is - they are the traditional source of info on long-distance bus schedules - Strætó is the local bus company here in the capital encroaching on their turf. A bit of competition never did any harm of course!
In fact I went and checked - Reykjavik Excursions have a bus that leaves Hvolsvöllur at 10:15 and arrives at Skógar at 11:20 (the reason for the long duration is that they stop at Seljalandsfoss!) - the fare is only IKR 2000. It is of course a bit late to be starting your hike at 11:20 - if you intend to do it in one day - the alternative would be to arrive the day before and camp at Skógar. Still, it won't be getting dark till pretty late so you should have enough time.