I'd instead try to pair with people on solving a problem that translates well to the problem domain that you're trying to hire for. Anybody who's new to the industry is going to need a decent amount of support & mentorship starting out before they're able to contribute meaningfully to a team and working with someone for a day is a good way to figure out how much support they're going to need and what it's going to be like to mentor them. Bootcamp graduates would likely be open to a day of paid pairing to figure out if a job would be a good fit.
If you did want to go with the more traditional coding test route, I'd try and do something relatively concrete:
- download a set of log files & group them based on a search
- hit an API route & use that to render and update a list of items
- connect to a database, figure out what schema migrations are necessary to support a new feature, and then talk through how to do the migration
- figure out why a test is occasionally failing on a CI server
- add metrics, logs, tests, and alerts to a service with two routes (/healthcheck and /doSomethingImportant)
Like all interviews, the closer the interview maps to the day-to-day of what your needs actually are, the better it will be. There's something beguiling about questions about dynamic programming or red-black trees, but being good at answering those questions has almost no relationship to day-to-day work. (Unless you're at a place where deeper knowledge of data-structures and computer science really matters... and in that case, you're not going to have much with recent bootcamp graduates anyways)