The bridge is either there or it isn't -- if it isn't, then it is too late to reinstall it and you will have to do the entire downgrade shenanigans from scratch.
...
Just reboot your Kindle to make sure the bridge executes and re-enables KUAL, then use your existing KUAL to reinstall all update_*.bin style hacks.
If that doesn't work, you must have forgotten to jailbreak properly in the first place.