Will NextDNS work with a bonded internet connections?

If your router is using DoH or DoT or IPv6 for upstream dns request then you don't need to worry anything because it doesn't need linked IP, so it will works fine.

If by any chance your router can only use standard IPv4 dns then your router must have the ability to choose routing through specific Internet connection for specific address to make it works. The way is simple you just need to make a new configuration for your nextdns account, the link is on the upper left of your homepage account. After that just link both of your IP, first configuration for first internet connection and second configuration for second internet connection. You can either link them using 2 ddns, or simply schedule the router to hit it each specifically.