Is this the first time you've gone to the house? If it is I don't know what's happened with your game but if you've just brought the Bridge Worker to the trading post Linebeck will be talking to him next to the broken bridge.
Yeah, the first time I went there I didn't see him. I've gone a few more times and he still didn't show up. I've met the bridge worker, but I never took him to the Trading post yet. Thanks for replying, Sheikah Warrior
You have to get closer to his table. I went there before getting the bridge-worker and he showed up when I got closer to the table. If it still doesn't work, then you might've done something wrong or your game is broken.