135,000 miles is the cost of a roundtrip award in Business Class:
https://www.aa.com/i18n/AAdvantage/r...iondefinitions
On AA the lowest award cost is 90,000 roundtrip for economy class.
On UA the lowest award cost is 85,000 round trip for economy class:
http://www.united.com/web/en-US/apps...ardTravel.aspx
Personally, unless there is something one wishes to do in AUH/BAH, I'd look for another routing. With a total of 10-12 hours connections, one might as well find a routing that will allow one to have that entire time as one block so that one can actually sleep or explore the connecting city.
If you do travel through BAH, do not drink the tap water in the airport and be aware that taxis may employee creative fares.
To get to BGW you will have to fly one of the following routes:
CAI-BGW on MS (UA Star Alliance partner)
IST-BGW on TK (UA Star Alliance partner)
AMM-BGW on RJ (AA One World partner)
DOH-BGW on QR (AA One World partner)
BAH-BGW on GF (AA bilateral partner)
Do note that for security reasons, flights to/from BGW may often cancel at the last minute. The airline may provide hotels, but in case they don't do note that hotel costs at BAH & DOH will be higher than those in AMM, CAI, & IST. But do note in all cities prices may very significantly depending upon hotel class.
If you want to fly nonstop to your gateway city, TK provides LAX-IST nonstops and QR provides LAX-DOH nonstops.
Travel via CAI requires a connection at JFK, YYZ or in Europe.
Travel via AMM requires a connection at ORD, DTW, YYZ, JFK or in Europe.
Travel via BAH requires a connection at AUH, DOH, AMM, or in Europe.
What class do you want to travel? What dates are you looking at?