If you migrate to the new Roblox chat, TextChatService, you can easily configure the Bubble chat bubble to appear above.
To migrate: Find TextChatService in your explorer, change ChatVersion in the properties tab to TextChatService.
To configure bubbles: Find BubbleChatConfiguration under TextChatService. Then tweak the VerticalStudsOffset until the chat bubble is above your GUI.
Note that if you’ve created chat tags or chat commands with the legacy chat you will have to rewrite them. You should migrate to the new text chat service because it’s more secure and modern.