From Phrases, Cliches, Expressions on www.joe-ks.com:
For the birds
Meaning: Something that is worthless.
Origin: Before the advent of cars, one could
see and smell the emissions of horse-drawn wagons in New York. Since
there was no way of controlling these emissions, they - or the
undigested oats in them - served to nourish a large population of
English sparrows. If you said that something was for the birds, you're
politely saying that it's horse crap.
Example: His
apology, after his deliberate and harmful actions, was for the birds
in everyone else's eyes.
...and then there are the following two quotes from the Bible which if interpreted the same way, would put the usage way before the 20th century:
Isaiah 18:4 For this is what the Lord has told me: “I will wait and watch from my place, like scorching heat produced by the sunlight, like a cloud of mist in the heat of harvest.” 18:5 For before the harvest, when the bud has sprouted, and the ripening fruit appears, he will cut off the unproductive shoots with pruning knives; he will prune the tendrils. 18:6 They will all be left for the birds of the hills and the wild animals; the birds will eat them during the summer, and all the wild animals will eat them during the winter.
Jeremiah 16:4 They will die of deadly diseases. No one will mourn for them. And they will not be buried. Their dead bodies will lie like manure spread on the ground. They will be killed in war or die of starvation. And their corpses will be food for the birds and the wild animals.
(from the website: 10000birds.com as an answer to the question, "Why is 'for-the-birds' a bad thing?")
I think it's probably just because in British slang pull has that meaning independently of bird. From OED...
pull: trans. 12a: Brit. slang. To pick up (a partner), esp. for sexual intercourse; to seduce. Also intr.
It also occurs as a noun in the expression on the pull, and there's no reason why a couple of young British men shouldn't hope to pull some girls on a night out. Come to that, the girls they end up with may have gone out hoping to pull some blokes.
As to why young British women are called birds, OED says it derives in part from a now-obsolete
burd: a poetic word for ‘woman, lady’; the female counterpart of berne n.;
in later use chiefly = ‘young lady, maiden’.
berne: a warrior, a hero, a man of valour;
in later use, simply one of the many poetic words for ‘man’.
Of chick, OED says applied to human offspring; = chicken n.; esp. in alliteration with child. Sometimes as a term of endearment, with citations starting from 1320. But their earliest citation for the current (well, hopelessly "dated", imho) sense girl; young woman. slang (orig. US) is 1927.
Best Answer
It appears that 'doing a bit' goes back to the early 20th century as a term for serving a prison sentence.
http://en.wiktionary.org/wiki/bit#Noun
'Bit' meaning a short span of time goes back to the 17th century, and presumably that's how it became associated with prison in the first place. "I've got to do a bit of time in prison."
http://www.etymonline.com/index.php?allowed_in_frame=0&search=bit&searchmode=none
I can't find any real resources as to where 'bid' came from directly, so I would assume that it is simply a result of the word shifting slightly once having gained distinct enough usage separate from its origins.