I haven't tested this, but you should be able to sysctl -p to reload the config instead of rebooting.

Just loading the sysctl values will not switch the packet scheduler on already existing network interfaces, but it will start using BBR on new sockets.

Switching the scheduler at runtime using tc qdisc replace is possible, but then you need to take extra care if the device is multi queue or not. Instead of explaining it all here just rebooting is probably simpler.