I defeated Watchdog of Old Lords, chalice dungeon Pthumeru level 3. But now I can't find anywhere else to go. I opened a new chalice ritual, which sent me to Central Pthumeru, where there are two of those electric centipedes, but I've done that area. I find this chalice dungeon thing confusing - very fun - but confusing.

I need more ritual blood to open a root chalice dungeon. I assume I may get the ritual blood from defeating Rom. Otherwise, where do all the other chalices come from?

thx much

You can go to defiled chalice or hintertomb, your choice but i recommend the latter since the defiled chalice is one of the most difficult dungeons in my opinion since you can be one shotted by anyone and thats because your health is cut down to half in this dungeon.

The other two chalice types (Loran and Isz) are from bosses that are only available after Rom.

Also, I don't think you ever have to do a root dungeon. Only the non-root dungeons contain progression-related items and bosses.