Learn Dutch: Ik zie een patroon, dus er moet een verband zijn. - I see a pattern, so there must be a connection.

Yes, but just like in English, moeten can also express a logical deduction. When you say er moet een verband zijn, you aren't saying the connection is required to exist, but rather that you logically conclude it exists ("there must be a connection").

Why is the word order dus er moet instead of inverting to dus moet er?

The word dus (so) is a coordinating conjunction, meaning it connects two sentences without messing with their word order. You just start the second clause normally with the subject (er) followed by the verb (moet). If you used a word like daarom (therefore), you would need to invert: daarom moet er...

Why do we need the word er in the second part of the sentence?

Here, er acts as a placeholder subject, exactly like "there" in the English phrase "there must be". In Dutch, when you say that an unspecified thing exists (like een verband), you pair er with the verb zijn.

I thought verband meant "bandage". How does it mean "connection" here?

The word verband comes from the verb verbinden (to connect or tie together). While it can mean a physical bandage, it is very commonly used for abstract links, relationships, or connections between ideas or events.