There is no evidence that the Prophet was bipolar or ever acted in a way that could be considered as suffering from a mental disability. He shouldered tremendous responsibilities - personally, religiously, and as leader of state - and it is truly amazing how he managed to balance all of those responsibilities while at the same time maintaining an intense personal schedule of worship.
However, given that receiving revelation is said to have been a heavy thing, I can understand why one might be tempted to draw a sort of mental parallel. In many cultures, there has been a thin line between spiritual vision and insanity - not the least because, to a very mundane person with no interest or belief in the spiritual realm, someone speaking on behalf of the divine is often considered insane!
It seems reasonable to treat these terms as mostly literal. Majnun, rather than meaning "mad", likely refers to the ancient practice in the Mediterranean and other regions whereby oracles, soothsayers, and so on, used to claim to transmit information from jinn or spirits. Thus, they are accusing the Prophet of being possessed and receiving the Qur'anic text from something other than God. However, God corrects them and says that this is not the case and that the revelation is actually from God. Some of the Sunni hadith texts refer to this view held by some disbelievers. Some may also have meant it in the sense of "that's crazy", but not necessarily as an expression that he was suffering from a psychiatric condition.
Similarly, some people who did not accept Islam accused the Prophet of bewitching people to follow him, and advised people not to listen to the Prophet speak so that they would not become bewitched. One of the companions even plugged his ears so he wouldn't hear the Prophet before eventually listening and becoming a Muslim!