You can add a new bookmark on your Mac easily enough, but to alphabetize, it's inexplicably difficult. Solution: add the new bookmark in Mac and then alphabetize in Safari on the iPhone. Here's how:
1 - Open Safari on your iPhone and click the Bookmarks icon (looks like an open book on the bottom left)
2 - Choose the folder where you've saved the newly-created bookmark and click Edit (bottom left)
3 - Using the icon appearing to the far right of the bookmark you want alphabetized (looks like three short lines on top of each other), drag it so that appears in the order you desire.
4 - Click Done (bottom right) and then click the next "Done" option at the top right of the screen.
If your Mac and iPhone are linked via iCloud, bookmarks alphabetized on the iPhone will be alphabetized in Safari on the Mac. You can also just add the new bookmark and alphabetize in Safari instead of first adding the bookmark on the Mac. Again, changes on one device will appear on the other if they're linked via iCloud. This also works for folders you want alphabetized.
Dear Apple: Please make alphabetizing on the Mac as easy as it is on the iPhone. At the very least, please don't change how easy it is on the iPhone. 🙂