With a horn, it's different. Horns are made of metal and are going to rust if you allow them to get damp. Plus, India? That's one of the absolute hottest and most humid places on earth. That's an apples to oranges comparison.
To the OP - don't worry about sweating on your bass. Unless you're sweating so much that it's the equivalent of dumping buckets of water on your instrument, just go ahead and wipe it down after a show and you're fine.
I think a bigger problem with wood instruments here in the northern hemisphere is them becoming dry and cold and the wood cracking. I had it explained to me thusly: your guitar is made out of wood, which is essentially plant tissue. Your guitar still thinks it's a tree. It wants just a bit of warmth and a tiny bit of moisture to keep it supple so that it's not so dried out that it's cracking. Remember that.