How does a bootstrapping startup organize an exceptional team with no budget?

This is a typical problem with any start-up, i.e. intention to trade everything for equity. I am assuming that you're trying to trade equity for cash. In that case I would suggest you to look out for individuals with diversified skills and competencies. The reason being, less the number of individuals less the amount of equity that would be required to trade.

Second option could be to look out for agencies to whom you could outsource the business process. I am not at all ashamed to mention that my own company is one such agency.

However, my only piece of advice to to try and add some retainership component to your model, apart from equity, as in a long term it's easier for people to lose motivation in absence of any capital gains. The reason being, people don't understand the value of equity in startup. Rather, the time it could take for that equity to turn into something big; it may not happen as well. That's why they say there's nothing called free lunch.

In my more than a decade experience working with entrepreneurs and helping them bootstrap, I have learnt that the market out there is crowded with individuals with a lust to join startup as a equity holder. In a short term, they may speak all those rosy language that may sound like coming directly from the Horse's mouth. But, in a long term you realize not everything is hunky-dory.

As far as finding a co-founder or a CTO or any other executive team member is concerned, ensure that you put down the roles and responsibilities attached with each title. Apart from above, ensure that you communicate your expectation lucidly and understand the values everyone is required to bring on the table.

Usual people who could be a good fit for you, apart from any agency, are people who aren't big on title.

Is there anything specific you're looking at? Please feel free to revert with more clarity to receive clarity. I am just a call away. All the best!!