Strictly speaking, a disk can use MBR or GPT, but not both. That said, there's an ugly and dangerous hack, known as a hybrid MBR, which is most often used on Macs, that enables a GPT disk to include MBR pointers to three of its partitions for the benefit of GPT-unaware OSes. There's very little or no reason to use a hybrid MBR except on Macs that are dual-booting with Windows 7 or earlier, or with other non-GPT/non-EFI OSes. A hybrid MBR would provide NO benefit for your specific case.
Be aware that boot mode (EFI/UEFI vs. BIOS/CSM/legacy) and partition table type (GPT vs. MBR) are not necessarily linked. Windows ties the two together, and older OSes understand neither EFI nor GPT, but other than that, you're usually free to mix and match. You can install Ubuntu in BIOS mode to a GPT disk, for instance. That said, using GPT for EFI-mode booting and MBR for BIOS-mode booting will minimize the risk of running into problems, but it's often possible to cross those boundaries if doing so is necessary. Thus, if you want to have a USB drive that's bootable under either BIOS or EFI, you can, in principle, use either MBR or GPT on it. You'll have to be sure to install both BIOS-mode and EFI-mode boot loaders, but the partition table can be either type. This type of configuration can be tricky to set up, though, and offhand, I don't know of any site that provides step-by-step instructions for configuring it. There are about a million special cases that can create problems for specific computers or for computers configured in particular ways (Secure Boot issues, firmware that's finicky about partition tables, 32- vs. 64-bit systems, etc.). Thus, depending on your needs, it might be better to plan on creating two or more bootable USB drives. Yes, that's more hassle to carry around and keep them straight -- but that hassle may be less than the hassle involved in navigating the mine field of quirks involved in creating a truly universal boot medium.