On commercial airliners, what happens when a pilot or co-pilot needs
to exit the cockpit to use the bathroom. Especially on international
flights, or even on small   regional jets. Are there protocols in
place? If so, what are they?

I doubt that all the details of such protocols are available to the
public. I did find this:

"Because their law enforcement authority begins and ends on the flight
deck, pilots are required to stow their guns in a locked metal box
whenever they're out of the cockpit.

At a minimum, most pilot groups want to get rid of that requirement
and allow pilots to wear guns in holsters, like other law enforcement
officers.

'If you (leave the cockpit) to go to the bathroom, you have to take
the gun off and put it in the box,' said Steve Luckey, a retired pilot
who chairs the national security committee of the Air Line Pilots
Association, which represents pilots at United, Continental, Delta and
Northwest airlines, among others. The restrictions force pilots to
handle guns more often, increasing the chances for an accident, he
said."

http://www.infowars.com/articles/2nd_amendment/only_small_percent_pilots_armed.htm

For years it has been assumed that El Al pilots have access to a
private restroom facility:

"El Al's pilots enter the cockpit before the flight and are sealed off
by doors of reinforced steel. They do not emerge from the flight deck
until every passenger has deplaned at the destination airport. Some
industry pundits claim that El Al's pilots also have access to guns in
the cockpit, but El Al refuses to comment on this issue. The airline
also will not reveal how pilots are fed and allowed access to rest
room facilities, but it is assumed that there is a separate bathroom
and small galley that can be accessed from only the cockpit."

http://www.avweb.com/news/safety/182978-1.html

They go to the washroom. That's why (amongst a lot of other reasons)
there's always another pilot.  I've been many flights and have
relatives who are pilots for major and minor carriers.  They all go,
if they have to.

On a recent flight I was sitting in first class when all the stewar...
er, flight attendants congregated at the front of the plane. They
turned off the lights in the front passageway and moved serving carts
to block the aisle at the head of first class and at the beginning of
the alcove leading to the flight deck. Then the flight deck door
opened and one of the flight officers emerged, went around the first
cart and into the front lavatory. Moments later, he exited and went
back to the cockpit. The blocking was undone, lights turned back on,
and the whole freakin' plane knew the co-pilot had taken a leak.

Better than bringing a milk bottle.  Get all that fancy electronics wet, no way.

On my little yacht, I carry a hospital type pee bottle. On a crowded
waterway, it is not proper to stand on the transom and " do it in the
bay"

Especially if it's cold outside.

|"El Al's pilots enter the cockpit before the flight and are sealed off
by doors of reinforced steel. They do not emerge from the flight deck
until every passenger has deplaned at the destination airport. Some
industry pundits claim that El Al's pilots also have access to guns in
the cockpit, but El Al refuses to comment on this issue.|

I love that one - I've been in El Al cockpits many times

As for the guns, you can be sure there are guns onboard, very
sensible, but they are in competent hands.

On larger aircraft the cockpit door is in front of another loo, which
makes a lot of sense. eg: the pilots have a private loo.

Some years ago British Airways tried to abolish this, in order to get
one more row of seats. The pilots nearly went out on strike.
I found it incredible that top management could be so thick.

On smaller aircraft there are normally two loos just outside the
cockpit, and a curtain, a flight attendant draws and guards the
curtain when the pilot/co pilot needs to micturate.

From what I've seen, being a pilot is a pretty boring job, very
sedentary largely a matter of the two keeping each other awake.

I've also been amused to see that 747 pilot seats tend to be quite
knackered, and suspect that the pilots prefer them that way.