We stayed at Seef Residence when we first moved to Bahrain and it was great. Not sure on the expense vs. hotels but worth a look.
http://elite-seef-residence.hotel-rez.com/index.htm?lbl=ggl-en
Try these guys. They were the only place in Bahrain I managed to find A4 Suspension Files for my filing cabinet. The Gentleman called Kumar was great, knew exactly what I was talking about and even delivered them for me.
http://www.alrashidbahrain.com/contact.html
I found them from this website in the end, which may help you as another "yellow pages" of Bahrain
http://www.bahraindirectory.net/officestationary.html