Personally I don't mind the overhanging tree at all. I think it gives the bridge some context - serene surroundings - if you see what i'm trying to get at. But of course shoot the bridge from differing angles and try shooting the opposite side of the bridge as Stevekin suggests.
I think the second close-up of the bridge is an improvement over the first. Though I think the best way to improve it yet again is to shoot at a different time of day - and on a day when the light is quite as flat and dull as it appears to be here.
I think you'll definately get worthwhile photos out of this location (even better then those you already have) if you keep shooting there!