Norm,
The idea of doubling the mainline, braid especially, is to give the best advantage to the leader ie the braid not to cut into the leader, and also due to the doubling of the mainline surface area, increases the joining knot strength by a large margin.
The Bimini is like all knots and while people claim that it retains 100% of the strength of the mainline, it usually does not. There are a few guys I'm aware of who are very proficient at tying the Bimini, and they can usually achieve about 90%. These numbers have been tested professionally, and mine tests at about 70%.
The only way of getting really close to 100% consistently is to buy a Paulus Bimini Aid. Also, check out this site for heaps of information regarding lines, knot tests etc. It is a real eye opener and one where you can put a heap of ideas into practise to improve the most basic of fishing skills, staying connected.
http://www.pcwi.com.au/fishing/index.htm
The major benefit you would achieve by using a double, it to retain the maximum possible from your rigs, so you can put more pressure on fish and know wth a fair degree of confidence, that everything will and should hold together.
A double will also allow you to use things like wind on leaders like the Egrell style, the Knotted Dog type or the ever increasing number of other over the counter wind on's.
If you're a fan of the Improved Albright, the doubling of the braid helps enormously with regards to knot strength.
Braid, by nature, is quite abrasive and a single strand of it under pressure, can cut mono and flurocarbon leaders due to it being so thin. However, by doubling it up, this problem is all but eliminated and once where knots were coming apart under pressure from either a fish or even due to casting pressure, the entire rig is far more secure.
Really, considering the beasties you're targeting, I think by mastering the Bimini double, you will put the odds a lot more in your favour.
I hope this helps.
Tim