No medical insurance included in package - is that okay ??

I guess "more than adequate" would depend entirely on a) the healthcare you are used to and b) what health issues you will face here. As neither fact is known to us, it's impossible to answer your question.

For me, if an employer thought saving money more important than assisting employees when their health fails, I would move on and find another job even if I was single. With dependents, I definitely wouldn't take it.

It says more about your prospective employer than it does about the health system in bahrain.

I would negotiate and get medical insurance for sure.

Yes government hospitals are ok, but they aren't always open at 2am for an emergency.

There is no negotiation - that's it ! Does anyone know of any good insurers ?

There are many, but it may cost you more than BD 1.000,00 per year/per person (depends on the clauses you want). For family, I guess they may give you some discount.

I have had to look into insurance recently and got a very quick reply with quote from Axa (http://www.axa-gulf.com/bahrain/en/Health-Insurance).  You might find it helpful to contact them to get an idea of the cost of coverage if you need to cover it yourself!