Caesar's supposed sexual relations with Nicomedes are related by Suetonius, who actually discusses the various versions of the charge at some length. Suetonius claims that the rumors began because during Caesar's embassy to Nicomedes in his youth he took so long to return to Thermus, under whom he was serving in Ionia, that suspicions of his actions were raised. Suetonius quotes Licinius Calvus as saying:

Bithynia quicquid et pedicator Caesaris umquam habuit.

and Caesar's troops supposedly sang during his triumph:

Gallias Caesar subegit, Nicomedes Caesarem:

Ecce Caesar nunc triumphat qui subegit Gallias,

Nicomedes non triumphat qui subegit Caesarem.

There are other instances that Suetonius speaks of, but they're basically all the same. That Caesar was intimate with Nicomedes seems undeniable--Caesar himself never denied it--although whether their relationship was sexual is rather less certain. Attacks on Caesar regarding his relationship with Nicomedes are limited to political slanders of the type that were common in Roman politics--Cicero, whom Suetonius quotes as having brought up Nicomedes several times, was pretty famed for his slanders, and several of his speeches are like four-hour long tirades of invective. But we need not necessarily take the repeated insults of Caesar's enemies any more seriously than Cicero's accusations that Clodius slept with his sister or that Piso was addicted to orgies since he was an Epicurean. More damning is what his soldiers said during his triumph, but that may well just be camp gossip, who really knows. Suetonius calls Caesar's relationship with Nicomedes his "contubernium." Contubernium is literally the sharing of a tent by soldiers of the same unit, but it can mean several other things. It is often used as a euphemism for "comrade," or "buddy," and it describes an extremely close relationship, such as the kind that soldiers who rely on each other to survive have. It is also used regularly to mean the tutor-pupil relationship that a junior general has with his senior, which may be the kind of thing that Suetonius is talking about. Lewis & Short cite two specific instances of its use to mean "concubinage," noting that it is here different than the usual "conubium," which describes a man and woman living together sexually--one instance is from In Verrem, and the other is the passage of Suetonius' where he says they were tent-mates. I'm not totally convinced that Suetonius isn't trying to play a double innuendo here (and Lewis & Short note that the use is ironic)--he may be implying that either Caesar was learning under Nicomedes or he was learning (wink wink say-no-more) under Nicomedes, depending on whether you believe the gossip or not