Catch the Marmaray east in the direction of Gebze . A ticket costs roughly 5.20TL (~USD 0.92) as of June 2019, and you must use an Istanbulkart which you presumably have. Get off at Osmangazi Station (two stops before Gebze) as this is closer to the D-100 highway that will carry you east. Walk roughly 300m north up the road from the station until you get to the circle-underpass junction with the D-100 highway. A nice position just after the start of the on-ramp, where cars are still moving slowly, should score you a ride in minutes.
However, the majority of traffic here seems to be going to Izmit, which is past the bridge. Turn down rides if you have to until you get one going over the bridge, to Yalova/Bursa/İzmir etc. If you're really stuck, take a short ride and ask your driver to drop you off on the side of the road at the off-ramp going to the bridge, and continue hitching from there or after the interchange. If you're really stuck on that road leading up to the bridge, you'll have to walk a few km along it until you get to the Petrol Ofisi fuel station, about a Kilometre before the bridge. Hitch at the on-ramp to the highway from there.