Why leave King's Landing now?

There are a lot of answers that draw knowledge from the Books, but from what I can gather the TV series is carving its own narrative.

As an answer from the TV series only;

Varys agrees to help Tyrion escape, and expects this to happen to schedule.

When Tyrion delays this, by paying his father a visit, he changes the circumstances of the plan, including its timing. Under the original plan Varys had prepared, there would have been plenty of time for Tyrion to have been escorted to the docks and for Varys to get back, removing a calculated amount of suspicion. When the alarm sounds, Varys would have had to sneak back in to the Red Keep and create a last minute Alibi. He may or may not know what Tyrion has done; but he knows something... I think Tyrions actions have forced his hand. Varys didn't intend on leaving Kings Landing at that point in time, but circumstances left him no choice. His mind was made up on the jetty, and not a moment before...

I'll try to answer this question, although spoilers will be rife.

Who does Varys serve? Remember back to his conversation with Ned Stark in Season 1:

Eddard Stark: "Tell me something, Varys. Who do you truly serve?"
Varys: "The realm, my lord. Someone must."

Varys may or may not be lying. We don't know. Up until now though, we know that he is playing a game, like Littlefinger and all the others. We also know that he knows much more about Daenerys than he lets on.

Arya Stark, again in Season 1, overheard him talking underneath the Red Keep to Illyrio Mopatis, the man who was looking after Dany and Viserys. At the time, their conversation is confusing, but as the series' continues it becomes more and more obvious what they were discussing. From the wiki:

...Illyrio pays a secret visit to King's Landing where he discusses their mutual plans with his ally, Varys, in the secret passages under the Red Keep. Once Khal Drogo's son is born, the Dothraki can move to invade Westeros and Viserys can retake the Iron Throne. However, Westeros must be in chaos and civil war before this happens. When Varys warns that a civil war, launched by a conflict between House Stark and House Lannister, is imminent, Illyrio becomes concerned that things are moving too fast, but Varys suggests motivating the Dothraki to move faster might be a viable strategy. They talk about how new Hand of the King, Eddard Stark, now has the same genealogy book that his predecessor read, and has met Robert's bastard son Gendry: the same evidence which led Jon Arryn to discover the truth about Queen Cersei's children. They discuss the possibility that the same fate may befall Lord Stark as did his predecessor.

This is incredibly important and was revealed very early on in the series. Whilst Robert wants Dany killed and Varys agrees quietly, he has no intention of doing this. Spoilers:

He is revealed in the books to actually warn Jorah Mormont that this is the King's intention and to be careful. The poisoner in Season 1 acted on his own accord, not on Varys'. See this question for more information.

Now, in the books all of this isn't revealed until Book 5 - the series is very premature in showing us all of this, revealing it all by midway through Season 1.

However, since it does reveal it all, we know that Varys' has plans for Daenerys and is in league with Ilyrio to protect her (for what end and reason, we don't know beyond his supposed desire to serve the realm).

Now, all of this is spoilerific and describes books 4 and 5 (and thus likely Season 5):

In the books, Cersei effectively rules as Tommen is too young. She is paranoid, incompetent and surrounds herself with allies who give her poor advice. Jaime grows distant from her. In the books, there is a Lannister, Tyrek, who disappears during the riot of King's Landing shown in Season 2. Jaime begins to suspect Varys had a part in this. There is also some speculation that Varys had some part in a puppet show that begins to be shown in the capital, discussing how a kingdom is ruled by arrogant, greedy lions. A stag stands up to them, but he is eaten. Finally, a dragon hatches and burns all the lions. Cersei is outraged. She puts to death the creators of the show, takes half the wealth from anyone wealthy who watched it and takes an eye from those who don't have wealth.

Following these minor mentions of Varys, in Book 5:

Kevan Lannister effectively takes control of the kingdom after Cersei is ruined. However, Varys enters Pycelle's chambers and kills him, before finally using his little birds to have Kevan Lannister summoned and killing him. He basically tells him this is because he is doing too good a job reversing all of Cersei's incompetent and moronic actions. Her actions are sowing rife and discontent between the Lannister, the Tyrells and leaving the realm open for the taking. There is another heir to the throne (besides Dany - more spoilers!) and he intends to make the realm ripe for the taking.

So after ALL THAT, including many spoilers:

His leaving the realm is consistent with his overall plan. When he sees Tyrion leaving, he knows it is a good time to leave to. His overall plan is truly underway and he knows Cersei, now mad with power and rage, will continue to ruin the realm. With Stannis far away, Renly gone, the Starks gone and the Tyrells and Lannisters fighting, it's the perfect time for his long-in-waiting plan to finally be put into full swing.

So in a show sense, there isn't much to go on until Season 5 airs in 2015 (and if I can help it, when I will revisit this question).

There can be some speculation as you said that he might be implicated in releasing Tyrion, being a past friend of him and Jaime is essentially immune (in a sense) to Cersei's madness.

However in the books:

He vanishes without a trace. And later does not return in the books until near the end of A Dance With Dragons So Varys going on the ship with Tyrion actually fits the story well and gives context to where he might have been.