Bahrain is a Muslim country, so people generally dress conservatively.  However, Bahrain has always been open society so it is generally very tolerant provided that you are respectful.  In general, Bahraini's love to dress up.  So try to look as good as possible wherever you go.  Clothes must always be ironed!

Use this as a general guide:

MEN

Mosques:  No shorts.  Clean clothing.  No sleeveless tops.  Shoes are not allowed when you're in the mosque.  Make sure you smell good but nothing overpowering (just shower and wear deodrant.)  Talk quietly when you're there.

Traditional Areas:  For the central market clothes can be less formal.  Make sure you don't wear something too nice because it might get dirty.  For everywhere else see malls and restaurants. 

Malls and Restaurants:  No shorts.  Make sure you look good.  Messy clothes are a big no.

Beach:  Shorts okay.  No speedos

Private Homes:  Unless ur invited to an informal garden party or a pool party then don't wear shorts and dress up.

WOMEN

Mosques:  Hair, arms and legs must be covered.  Loose clothing required.  No shoes allowed inside the mosque

Traditional Areas - Souq, villages, central market, etc.:  Skirts should be below the knee but long skirts and pants are preferable.  Short sleeve to long sleeve tops preferable.  No spaghetti strap tops and no cleavage. 

Malls - Seef mall, A'ali mall, dana mall, bahrain mall etc.:  Skirts below the knee.  Short sleeves.  No spaghetti strap tops and no cleavage.  Malls are usually crowded and people from all walks of life are there.  You can wear whatever you want but the more you show, the more guys will stare, so its best to cover up.  In the mornings though, when there are less people, you can wear slightly less conservative clothing.  People are usually dressed up at malls. 

Restaurants:  Depending on the restaurant, spaghetti strap tops and some cleavage is okay.  Generally if the restaurant in in Adliya or in a 5 star hotel then less conservative clothing is required.  However, it it best to wear skirts below the knee.  People are usually dressed up at restaurants.  Make up is a must.

Beaches:  In private beaches anything goes except for nudity of course.  For public beaches, wear what you'd wear for a mall but of course there's no need to dress up.

Private homes:  Depends on how conservative the family is.  But generally bahrainis are tolerant of other forms of dress.  Note:  Bahraini women care a lot about facial and body hair.  Its best to get your eyebrows threaded and everything else either bleached or waxed. 

In general, Bahrainis are very tolerant people.  However, the less bahraini you look, the more tolerant they will be of your clothing.  However, if you are in a crowded place like a mall then expect a lot of stares and comments from men if you dress less conservatively than the other females surrounding you.