Without burning money you'll need to be creative. Either do it yourself or go sourcing the supply side. Can you go find a group of people you can use to transport things and basically sign up on the platform on their behalf and then hand stuff off to them? Maybe you know some travel group that exist and you could pay them to take packages. You're basically acting in an agency model in the beginning instead of being a true P2P marketplace. It's a common strategy though it does often lead to just becoming an agency because it's more successful than your organic marketplace. This would be like if you called an Uber and Uber calls up a private driving service to pick you up.

The only real example I can think of being bootstrapped is Airbnb, and even that wasn't bootstrapped for long.

Unless you have a good go to market strategy, you might want to try something easier.

At the risk of being overly critical, the cost of shipping packages is pretty low unless you're trying to do same day delivery, in which case Uber already lets you get your package delivered.