I don't use Twitter often, but here's my stab at a method for implementing this:
*Assuming the thing is called TweetTip. Could be anything. Just to get the idea across...
Step 1) tweet "#tip @bob 1BTC" to the TweetTip account (as suggested)
Step 2) TweetTip tweets back with a unique Bitcoin Address and probably "@bob 1BTC" so you know what it's for.
Step 3) You send your BTC to that address.
Step 4) TweetTip confirms that it has received the amount with a tweet to you.
Step 5) TweetTip checks bob's recent tweets for a receiving address (as suggested).
Step 5a) If found, send BTC to that address. Tweet to bob that he got a tip from @you
Step 5b) If not found, tweet to bob he has Bitcoins waiting! Link to TweetTip.org/HowToGetYourTip
Step 5c) Periodically re-check bob's feed for receiving address up to a maximum time limit (90 days?)
Step 6) Profit
So ... is this possible with Twitter's available API? And if so, does that make the most sense?
The most complicated step is 2&3. If the official bitcoin client had bitcoin:// URI support that'd make things a bit easier. TweetTip could tweet "bitcoin://receivingaddress/btcamount
" or whatever back and then it'd just be a matter of clicking and Accepting on the desktop client.
Anyway, thoughts? I'd be willing to take a stab at this if it sounds good to others.
EDIT: Or would this make more sense:
Step 1) Go to tweettip.org, type tiper's name, tipee's name, and amount.
Step 2) Send BTC to address that tweettip.org responds with.
Step 3) Once received and confirmed, TweetTip proceeds from Step 5 above.