Two different questions.

To maximize your efficiency, the best thing to do is get an aftermarket valve.  There are several nice valves that can drastically improve your efficiency.

But regardless of whether you keep your old valve or get a new one, you will want to optimize your in-line regulator pressure.  This is your main efficiency determinant for any given setup.

First, set the velocity roughly where you want it to be, using the IVG.  Fire a couple of shots over the chrono.  Then increase the pressure from the in-line reg.  Fire some more shots over the chrono.  If the velocity increases, turn up the reg some more, and fire again.  If your velocity at any point gets way over where you want it to be, use the IVG to lower it.

Keep firing and raising the pressure until raising the in-line pressure does not increase velocity any more - you might even see the velocity drop.  Basically, you want the reg set at the pressure where either raising or lowering the in-line pressure will LOWER your velocity.  That's your regulator sweetspot, and the most efficient setting.  You'll then have to change velocity again with the IVG to get your final velocity, and probably tweak the in-line pressure again.

Keep in mind that this pressure setting is only the most efficient for any given setup and any given velocity.  If you change the velocity a lot with the IVG your regulator will no longer be optimized (your gun will probably still work, just not as efficient).

Now, for increasing your bps, that's a bit more complicated.  Basically, you have to time the gun very tightly to get a super-short trigger pull.  There are two settings you can change - the hammer lug and the 3-way.  Backing out the hammer lug will make the sear trip sooner, which means less pre-pull on the trigger.  If you back it out too far, however, it won't engage on the recock and your gun won't work.  So you want it as far out as you can without getting a malfunction.

Then, the 3-way.  Some 3-ways have shorter throws than others.  The Orracle 3-way is pretty good, I don't know what comes on the BM.  But the 3-way is usually a main upgrade for mech cockers, for exactly this purpose.  Anyway - you want the 3-way set so that it recocks the gun as soon as possible after the hammer is released.  But if you set it to recock before the hammer moves, you'll have a problem - so you want to get it just so.

After you have done that, use trigger stops to avoid post-pull on the trigger, and you have shortened your pull as much as possible.

Other things that can help - roller sears, lighter trigger springs, reshaped hammer lugs, more comfortable triggers...   The list goes on.  But it all comes down to careful timing in the end.