Mojave USB Upgrade – How to Upgrade to Mojave with a USB Drive

Seems they added the installer recently to the new App Store on Mojave. If you search for macos mojave the installer shows up in the results under the "Utilities" category.

The simplest way to boot back to Mojave would be to reboot the Mac and immediately hold down the option key. This will invoke the Startup Manager. Select the Mojave startup disk. Next, click on the arrow below the icon to boot Mojave. If you wish to make Mojave the default, then hold down the control key before clicking on the arrow.

Apple a recently added new instructions for using the Startup Manager. These instructions can be found on the Apple website: How to select a different startup disk.

While it is technically possible to select Mojave directly from Mavericks, this would involve installing a third party boot manager such as rEFInd. Unless you intend to change operating systems often, such an installation would probably not be worth the trouble to pursue.