If, instead of a solid colour, you wish to make the background of your Quick Announcement Bar a gradient, you can do so with a few small edits.
This isn't an official feature, but it can be done.
Begin by expanding the message box by clicking More Options:
After you've entered you message, below it, paste this code:
background-image: linear-gradient(to right, #1ca1c9, #aceafc);
background-color: rgba(0, 0, 0, 0) !important;
From here, you can replace the colour codes. #E86712 and #f0d800 are the codes that refer to the beginning colour and ending colour of the gradient.
You can use this tool to help you find the codes to the colours you wish to use.
You could also place the code inside the theme.liquid <head> section. This can be handy if you have many bars and want all to have the same gradient.