The key to the scoring system is your B-shot. The bubbles 'stick' to enemies, this is important. The way to score is:
1) Hit a big enemy with a full b-shot. A fully powered up b-shot (the meter for your b-shot is down on the bottom of the screen, should say 15 when fully powered) will stick 15 bubbles of various sizes to the enemy.
2) While the bubbles are 'stuck' to the thing, kill it with your A-shot. This will trigger a multiplier equal to the number of "stuck" bubbles+1. This multiplier lasts a fixed amount of time, based on the enemy size. (See below, however)
3) The enemy will release some items upon death. Normally they are worth 100 points each. However, the multiplier from step 2 is applied to them. Even more importantly, the collection of these items INCREASES the multiplier time. Also of note: the multiplier applies to the base point value of any enemy you kill, even if it is just with the A-shot.
4) Keep doing this. You will discover after you 'chain' a few 16x enemy kills together and get the multiplier high enough, some enemies will release items tons of items even if you don't B-shot kill them. Not only that, the items will fall fast towards you. This is the real trick to scoring. Triggering this racks up points pretty quickly.
Another thing: Kill bosses the exact same way. (b-shot "stick" -> a-shot kill). This will cause all on-screen bullets to convert to items, and the same multiplier rule applies. The multiplier and the resulting timer will be in effect when you start the next stage. So convert a thick bullet pattern, collect to jack your 16x multiplier up, and then kill things for 16x points at the beginning of the next stage.
Getting lots of 16x chains/items requires fairly aggressive play.
Oh, one other 'advanced' technique. It seems that any bullets over/near an enemy with you kill it and trigger items will ALSO be converted to items. I think the explosion needs to touch them. If you watch any replays you'll note sometimes the player will exploit this.
There are also boss-milking techniques in this game, involving peppering a boss with the 'small' parts of the b-shot for extended periods of time.