In my opinion, Mind Blank is the mental version of the Antimagic Field. While it protects you from any form of mental contact, even from a Wish spell, it cannot see the difference between beneficent and harmful spells. It simply blocks all mental 'intrusions' like some firewall. Also note that no form of scrying works when you try to detect a Mind Blanked creature. As if he simply has ceased to exist. While the spell description doesn't say explicitly that Telepathic Bond will not work I felt that it was in the spirit of the spell to disallow all forms of telepathic contact. A Sending would work if the barbarian could do the sending, but he wouldn't be able to receive anything, as a Demand spell would also be blocked. Perhaps a Telepathic Bond could work one way, enabling the barb to send but not to receive. But there is also the question whether the wizard could target him with TB to start with, as MB wouldn't allow any contact to be established, the spell could be blocked without any effect. Following my reasoning, the barb's mind would simply 'not exist' for the TB to take effect on.