Not as easy as it sounds sometimes..depends on the handlebars and the handlebar stem..If the handlebars are all in one with the handlebar post then they may point forwards in a strange way making it rather odd to ride once you have turned them around to fold on the left side of the bike ..rather than in the middle..I just did it on an old folder of mine...Looks OK on mine because I have removeable handlebars and have put straight bars on...but the quick release for the height adjustment is now near my knees and in danger of stabbing me ..instead of out of the way at the front..
Easier idea would be to get a bigger bag..or try taking the seatpost out with the saddle and sticking that in the middle or in the bottom of the bag..Reduces the height of the bike in the bag..
Or..adjust the brakes so they point straight down when the bars are folded down..and that may make the whole package thinner..
Getting a bigger bag is easiest..I got a really good bag from a garden centre that was designed for carrying away leaves in the autumn..Bike goes straight in and it has a drawstring top..only a few pounds..Really heavy duty plastic reinforced nylon bag..