We crossed the bridge, with bike and panniers, in December. The path to the bridge has got plants indeed but was easy enough for us to cycle through. Maybe this changes in Spring or Summer.
The bridge seemed strong enough still, the wooden beams are supported by the steal ones underneath. Just at some time there's no wood and you have to carefully move your bike onto others etc. Slowly Slowly and with care and it's an amazing shortcut, we feel. Good luck