This certainly is possible---but unless you define the "several ways" to verify that A has the funds, the solution must exclude this key component. Here is one possible solution:
Special Multisignature Bitcoin-Address
Create a 3-of-5 multisignature Bitcoin address to which A transfers the Bitcoin in question. A owns 3 of the 5 participating addresses, whilst B and C contribute one each. Next A prepares a partially signed transaction that is signed with only one of his keys.
To eventually access the funds, B and C must both sign this transaction (or ask A for further signing). But it does not tie up the funds in that A can still access the Bitcoin using only his own keys.
Note that this only protects A from either B or C unilaterally taking possession of the bitcoins involved, but it does not offer any reassurance to B or C that the bitcoins will remain available to them in the future. That may create a particularly perverse incentive for intermediary B and recipient C to conspire into splitting the pot among them rather than adhering to whatever B's responsibilities in this matter were supposed to be.
I don't understand how this is different from just requiring all 3 signatures? – Nate Eldredge – 2014-04-08T21:34:55.190
@NateEldredge ok? please elaborate on what you are talking about , and how A can authorize a payment at Time0 to be pulled at Time1 from the partial signatures given to B and C. If all 3 signatures were required, then A would have to be present at Time0 and Time1 – CQM – 2014-04-09T03:38:42.140