Sprinkling soda to deodorise clothes in laundry basket?

I work out 5/6 times a week, and have an issue whereby my sweaty workout gear sitting in my laundry basket stinks up my room. I do try to let it dry out before putting it in the basket, but even so the smell is noticeable. Unfortunately, I live in a shared flat, so I can't just keep the dirty clothes in the washing machine between washes, and it's not feasible for me to put a wash on every time I work out.

I'm wondering if it would make sense to sprinkle some baking soda onto the clothes after I put them into the basket, as a means of keeping the odour down? The soda would then go into the washing machine with the clothes when it's time for a wash.

Maybe it's not the most efficient or cost effective solution, but I'm interested in hearing opinions on why it would or wouldn't work.