If you never intend to touch fiat at all you don't need to apply to be a credit union. Credit unions don't deal with commodities. You can just set that up as a club or non profit for tax purposes. Maybe apply for a 501c. Are you planning on being for profit or nonprofit?
The credit union is necessary to get a routing number to be used for direct deposit.
So you are planning on accepting deposits in fiat? I guess I got confused by franky1s post. A bank or credit unions routing number or numbers are used to identify a financial institution usually for the ACH and wire transfer system. The hurdles you will jump through to be a bank will require lots of employees and attorneys. If you are crossing state lines you will need to comply with interstate banking and branching laws which will add more employees. If you're going to deal with international customers too you may need to hire everyone on this forum to help. That's the reason these startups go out and secure big money investors first.
Seriously, I'm not sure you could ever accomplish that without being more expensive than Circle or Coinbase.
The main focus would be on the ACH to access the Electronic Payments Network which allows a "depository institution" as defined in § 19(b) of the Federal Reserve Act, 12 U.S.C. § 461(b), this includes "insured credit unions".
“Federal credit union” means a cooperative association organized in accordance with the provisions of this chapter for the purpose of promoting thrift among its members and creating a source of credit for provident or productive purposes;
The term “insured credit union” means any credit union the member accounts of which are insured in accordance with the provisions of subchapter II of the Federal Credit Union Act.
For a credit union maintaining less than $50 million in deposits it is not too difficult to maintain insurance on users accounts. Especially since the Bitcoin credit union would never hold any fiat in accounts. It would immediately transfer any funds into bitcoins or to another bank account for deposit.
You would need insurance on the amount you have in customers' accounts until you use the money to buy the bitcoin.
You also need to understand that a direct deposit is little different then accepting a check (the fraud risk is reduced however) as direct deposits can be reversed for a number of reasons. A direct deposit can be charged back and can be "nsf". These are pretty rare, and really only happen with smaller businesses but even then they don't happen very often because most businesses make paying their employees a top priority.
The biggest risk is getting a direct deposit that is initiated by the customer. A few banks allow this, ING direct (which is now owned by capital one) was one of the first banks that started this, but others have jumped on the bankwaggon. I understand that there is no balance requirement for a direct deposit to be sent, but it will be reversed by the issuing bank in the event of NSF in the sending account.