How did the Trinity Killer manage to leave no traces?

He was very thorough at cleaning. This is from the very first crime scene, during the kill:

And this is during the investigation:

Dexter comments on this: "It's a very well organized crime scene. The assailant took his time. Cleaned up after himself." with a funny remark "Obviously doesn't have kids".

Now, how exactly did he manage to clean the whole scenes is never seen, if I remember correctly. But note the different carpet color on the two snapshots. This is because, prior to his kill, Arthur put a big white towel over the original green carpet:

He has a ritual, not unlike Dexter's, and a certain preparation for the kill, albeit somewhat less efficient than Dexter's (since he actually has to clean some of the traces off the scene itself).

He might have left trace evidences in the bathtub like hair. But the cops had no reason to think that he would sleep in the bathtub with his victim. Also, they would have to drain the bathtub to get hold of the victim's body, which would mean whatever evidence was trapped in the blood to be flushed out. And even in case the cops thought of analysing the blood, finding a single hair in a bathtub-full of blood is no easy task.