Hmm .. that journey is surely more than just a weekend trip ?
Travelling by train + bus is the cheapest way of getting there. Mumbai (Maharashtra) to Ooty (Tamil Nadu) distance is 1167 km and you can get there by train + bus in just over 55 hours and 35 minutes. However, flight + cab tickets come also cheap with fares starting from ₹ 6267.
The weather is amazing right now. You'll have a great time.