It’s great to know that you are planning a cycle tour from Manali to Leh.
I shipped my bicycle from Leh via GATI (logistics company). It costed me about 3,000 INR to ship it to hyderabad. They charge you on volume of the box irrespective of the weight you put in the cycle box. I had my tent, and other misc stuff put in the cycle box which got shipped via Gati.. Let me know if that answers your question. You can call Gati (in Leh) at +91–9906993676