"When composing an email, many times a little bubble will appear next to the recipient's name. If I move over it, a menu appears. What this is?"

It's a Person SmartTag and you can disable in Outlook's Tools, Options, Other tab.

You may see something similar in the message body when you type names, addresses, or phone numbers and use Word as your editor. To disable these tags, either from Word or from the message form's window, go to Tools, Autocorrect, SmartTags and disable the tags.