Step 1: Understand the question.
We need the city that was not part of the trading and port network of the British colonial economy.
Step 2: Recall the background.
Under British rule, Bombay, Calcutta (Kolkata) and Madras became the three big port cities and presidency towns. They moved raw material out and finished goods in, so they were tied closely to the colonial economy.
Step 3: Check option 1, Bombay.
Bombay was a major port and a centre of the cotton trade. It was inside the colonial system. So option 1 is wrong.
Step 4: Check option 2, Kolkata.
Calcutta was the colonial capital for a long time and a key centre of trade and jute. It was inside the system. So option 2 is wrong.
Step 5: Check option 3, Madras.
Madras was a colonial port and administrative centre. It was inside the system. So option 3 is wrong.
Step 6: Check option 4, Bhopal.
Bhopal was an inland city and the seat of a princely state, not a colonial port or trading hub of the empire. It stood outside that port-city economic system, so option 4 is right.
Final Answer:
Bhopal was outside the colonial economic system, option 4.
\[ \boxed{\text{Option 4: Bhopal}} \]