The reason why your source code does not function as expected is due to utilising the TextChatService methods on the server.
The method ‘:DisplayBubble()’ is only available for the client therefore can be only used in LocalScripts or in Scripts with the RunContext set to ‘Client’ as stated in the documentation. (TextChatService | Documentation - Roblox Creator Hub)
Below is an example of LocalScript which utilises the method correctly.
Note: The example used here may be different to what your trying to achieve.
local Players = game:GetService("Players")
local TextChatService = game:GetService("TextChatService")
-- Only the client can see this. Meaning no other player will be able to see this.
Players.LocalPlayer.CharacterAdded:Connect(function(Character: Model)
TextChatService:DisplayBubble(Character, "Message 1")
end)