I would rather take streets than the north side trail on Arlington Blvd.
For the Memorial Bridge approach, I would take Irving to Pershing and right across 50 to south side trail rather than get on the North side trail.
For the TR bridge, I would take Irving, cut over to Highland, cross Clarendon/Wilson and make a right on Key. Left on Veitch and straight across Lee Hwy onto 21st/Scott and make a left on the Custis when returning to Lee Hwy. An alternate, which I would actually take but has more traffic, would be to take Irving to Clarendon, turn right down to Rosslyn and make a left on Lynn to the TR bridge. I prefer taking Lynn across the IoD rather than the Custis sidewalk as it eliminates the right turning car conflict.