The question is a good one, and worth discussing. My own sense is that it includes a mis-step, however, which casts a different light on things. My short answer to the question posed ("how does 'foot washing' lead to the act of 'sexual intercourse'?") is: it doesn't! First, though, to pick up a point made in a comment to the question.
"Feet" as a euphemism for male genitalia
As noted, it is very widely repeated that "foot" (Hebrew רֶגֶל regel) is a euphemism for male genitals. You can find this repeated all over the place. One example is made in the context of an interesting suggestion about irrigating Egypt "by foot" in an article published in 1988.
Virtually every commentary on Ruth 3 will spend some time on this possiblity, it adding to the frisson of Ruth's night-time encounter in the field with Boaz. So, for example, in Hubbard (p. 203), and Nielsen (p. 69), and Fentress-Williams (p. 89), and Goldingay (p. 180), etc.... It is, accordingly, often also so understood in 2 Samuel 11:8, as for example R.P. Gordon (p. 254) notes.2
I find myself a little hesitant in the Samuel text mainly because we're dealing with idioms, and not simply a single word. In the Ruth text we have the suggestive (from Naomi to Ruth!) to "uncover his feet" (וְגִלִּית מַרְגְּלֹתָיו Ruth 3:4). Fair enough. In 2 Sam 11:8, however, the instruction (from David to Uriah), to "wash your feet" (וּרְחַץ רַגְלֶיךָ). This idiom occurs 7x in the Hebrew Bible (Gen. 18:4; 19:2; 24:32; 43:24; Jdg. 19:21; 1 Sam. 25:41; 2 Sam. 11:8), and in every other case it looks like a straightforward ... washing of feet! (Gen 19:2 may be an exception here, but I'm not so sure.)3
This takes us on to the "mis-step" mentioned above.4
The David-Uriah Dialogue
I don't read Uriah's response about refusing to sleep with his wife as a response to the foot-washing invitation. This is the exchange:
11:8 David: Go down to your house, and wash your feet.
Some action now follows, with a report back to David. He's not happy, and has another interview with Uriah the next day:
11:10b David: Are you not come from a journey? why did you not go down to your house?
11:11 Uriah: The ark, and Israel, and Judah, abide in booths; and my lord Joab, and the servants of my lord, are encamped in the open field; shall I then go into my house, to eat and to drink, and to lie with my wife? as you live, and as your soul lives, I will not do this thing.
There is a considerable period of time intervening between David's foot-washing invitation, and Uriah's virtuous reply. I don't see them as directly related.
Why, then, does Uriah mention sexual intimacy? As commentators will note (both McCarter and Auld do - see note 2, below), Uriah's mention of the Ark reminds David (and the reader) that Israel's warriors are in a state of ritual purity while on campaign (Deut 23:10-11 [MT 11-12]), an observance that David in his younger days had been committed to (1 Sam 21:3-5 [MT 4-6]). This is the standard which Uriah is upholding.
That observation also tells against the "euphemism" reading, I think -- or else points to a highly veiled and allusive suggestion. Would David really blatantly lead one of his mighty men (2 Sam 23:39) into ritual impurity? He might though, in mentioning the "foot washing", have introduced the hint of double entendre.
Conclusion
Whatever decision one takes about the euphemistic value of "feet" in classical Hebrew, the flow of the conversation between David and Uriah, and Uriah's pointed claim to ritual purity is the better explanation (I believe) for what is going on in this text.
David is really sending Uriah home in v. 8 to enjoy the comforts of home, "foot washing" (literally) among them (see the other 6 occurrences). That a slightly woozy, slightly warm Uriah might just enjoy the evening with the (apparently) ravishing Bathsheba is a cunning bi-product of the joys of the domestic hearth. (After all, if David couldn't resist, how could her husband?) That Uriah should reply in terms of abstinence says more about his understanding about the ritual nature of the Israel's military campaigns, than it does about clean "feet".
- I'm citing the 1917 JPS translation throughout in this answer, lightly updated.
- Not with a preview in Google Books, also P.K. McCarter, Jr., II Samuel (Anchor Bible 9; Doubleday, 1984), p. 286; A.G. Auld, I & II Samuel: A Commentary (OTL; Westminster/John Knox, 2011), p. 457. Auld also notes that the main edition of 4QSama (Dead Sea Scrolls) reconstructs the text so as to read "and lie with your woman", which is also what Josephus has.
- Also, the enduring and careful work of S.R. Driver, Notes on the Hebrew text ... of the Books of Samuel (2nd ed.; Clarendon Press, 1913), p. 289 takes no notice of it whatsoever. I think it's safe to say Driver didn't see the "foot washing" as a euphemism.
- In an earlier form of this answer, I claimed that neither of the two main Hebrew-English lexica that I have available list the "euphemism" as one of the recognized meanings for regel. That isn't quite so. In BDB's case, there is still some Victorian reticence: but it does recognize the possibility in the case of Isa 7:20 (see top p. 920, col. a). HALOT (no online source for this) likewise makes brief mention on p. 1185, col. b, sub 4a, b relating to Ex 4:25; Isa 6:2; 7:20; also Jdg 3:24 and 1 Sam 24:4, all these quite specific cases (e.g., urination). But it is absent from Jastrow's dictionary, not normally the shy type. I still need to check the Dictionary of Classical Hebrew, but don't have it handy. And if anyone cares, neither is it in the range of meanings for Akkadian šēpu(m) "foot" in the voluminous entry of the Chicago Assyrian Dictionary.