I would highly suggest you consider what your near and long term bareboat sailing interests and destinations are before choosing a particular certification (ASA, US SAiling, ...).
If you are intending to do anything in Europe, like Croatia, Greece, etc they are becoming increasingly more strict on enforcing the EU sailing (and power) requirements. Requiring the "International Certificate of Competence". Also commonly referred to the major cert program "RYA Certificates of Competence". We were able to make an equivalency argument/documentation for my US Sailing (or ASA) certificates (via the Article 4 Paragraph 3 of The Ordinance on Boats and Yachts) for the Greek Ionian Sea area last year but it can be highly charter company specific as to what they'll accept. Sailing from Croatia from what I understand is getting extremely strict about needing the ICC. There is more emphasis on VHF skills, hands on demonstration of boats skills.
In short DO NOT assume that the Bareboat ASA 101-104 certs will accepted in Europe even if they say "bareboat". And do not rely on ASA or US Sailing saying they'll issue an ICC equivalent in the form of an "International Proficiency Certificate (IPC)". That IS NOT the same as the ICC. Some charters/countries will/may accept it and others will/may not. CHECK!!
Some charters will also let you do a local 1-day hands on "sea trial" course to certify you from an ASA104 to an ICC.
The other thing is finding an ICC cert program in the States is hard to find. Usually will have to go to someplace like Miami, Annapolis, Newport, Tortola, Bahamas.
NauticEd is a big ICC cert program worldwide using the RYA (British Royal Yachting Association) courses.
May be more of a hassle, cost a bit more but could save you time, money down the road.
Randy