user3456: Imagine that your opponent is away from the board and you want to make a move and then offer a draw and leave for the toilet with some urgency. What is the solution to this inconvenience? Can a player rely on the arbiter to go to the trouble of hunting for the opponent and passing the draw offer?

user1099: The correct way of offering a draw is, as you probably know:

Make a move 
Make an offer 
Press the clock

When your opponent is not present:

Make a move
Stop the clock (or you can leave your time running)
Call an arbiter and say that you want to offer a draw, and your opponent isn't here
Start the opponent's time
You are free to go now - if you run into your opponent on the way, you can mention the offer
When you're back at the board, make your offer.

Note that the draw-offer is perfectly valid at any given time. The reason why you call an arbiter to explain the situation is to avoid being accused of distracting your opponent when you offer it in "incorrect" way.
Edit: Adding information from official FIDE rules:

9.1.b.1: A player wishing to offer a draw shall do so after having made a move on the chessboard and before pressing his clock. An offer at any other time during play is still valid but Article 11.5 must be considered. No conditions can be attached to the offer. In both cases the offer cannot be withdrawn and remains valid until the opponent accepts it, rejects it orally, rejects it by touching a piece with the intention of moving or capturing it, or the game is concluded in some other way.

And

11.5: It is forbidden to distract or annoy the opponent in any manner whatsoever. This includes unreasonable claims, unreasonable offers of a draw or the introduction of a source of noise into the playing area.


3456: <p>Imagine that your opponent is away from the board and you want to make a move and then offer a draw and leave for the toilet with some urgency. What is the solution to this inconvenience? Can a player rely on the arbiter to go to the trouble of hunting for the opponent and passing the draw offer?</p>
 1099: <p>The correct way of offering a draw is, as you probably know:</p>

<ol>
<li>Make a move </li>
<li>Make an offer </li>
<li>Press the clock</li>
</ol>

<p>When your opponent is not present:</p>

<ol>
<li>Make a move</li>
<li>Stop the clock (or you can leave your time running)</li>
<li>Call an arbiter and say that you want to offer a draw, and your opponent isn't here</li>
<li>Start the opponent's time</li>
<li>You are free to go now - if you run into your opponent on the way, you can mention the offer</li>
<li>When you're back at the board, make your offer.</li>
</ol>

<p>Note that the draw-offer is perfectly valid at any given time. The reason why you call an arbiter to explain the situation is to avoid being accused of distracting your opponent when you offer it in "incorrect" way.</p>

<p>Edit: Adding information from official <a href="http://www.fide.com/component/handbook/?id=171&amp;view=article" rel="nofollow">FIDE rules</a>:</p>

<blockquote>
  <p><strong>9.1.b.1:</strong> A player wishing to offer a draw shall do so after having made a move on the chessboard and before pressing his clock. An offer at any other time during play is still valid but Article 11.5 must be considered. No conditions can be attached to the offer. In both cases the offer cannot be withdrawn and remains valid until the opponent accepts it, rejects it orally, rejects it by touching a piece with the intention of moving or capturing it, or the game is concluded in some other way.</p>
</blockquote>

<p>And</p>

<blockquote>
  <p><strong>11.5:</strong> It is forbidden to distract or annoy the opponent in any manner whatsoever. This includes unreasonable claims, unreasonable offers of a draw or the introduction of a source of noise into the playing area.</p>
</blockquote>
