I will try to be as concise as possible.
To start off with, if you find that your present workflow, image processing, and image finding/retrieval results are satisfactory and satisfying, then I would stick with it. I know many people that use the same products you do and feel it is the best suited for their workflow.
If on the other hand, you get discouraged, frustrated, or are otherwise unhappy with what you have to go through to accomplish your workflow, image processing, and image finding/retrieval results, then I would highly recommend looking at Lightroom. Also, if you find that you end up with multiple large (45 to 100 MBs each) files of the same image, and/or waste time figuring out which is which and what the difference is, Lightroom will be a very satisfying experience....once you learn how to properly use it and go through the ramping up process. It is a fairly complex product, as is PS, and you will need some time to become competent enough to realize the substantial time and space saving gains that are available.
Having said that, though, there are a few things to consider:
If you truly have very little time to devote to things other than your current workflow, and you still want to investigate the possibilities available in LR, I would highly recommend getting and watching the Lightroom 3 tutorial available on this site as the FIRST thing you do.
I DO NOT recommend getting the trial version and start playing with it to see if you like it. That would be a big time-waster and would most likely result in failure. I say this because the database management aspects are not the same as using PS and BB, and the first thing you will need to do is "import" your images into LR, which is not really importing at all. It's creating a catalog of references to where your photos live on you computer system. I will say that if you are a smart person that thinks in certain conceptual ways, you MIGHT get away with playing with it and come out the other side thinking you might like it, but it's a high risk, since once understood, LR is a fabulous tool for pro photogs. Spend the money on the tutorial, watch it, and you will KNOW whether you want to spent the time and money to convert your workflow to LR.
Also, round-tripping from LR to PS and back to LR is very nice, especially since you are familiar with PS. This process, though, is a case where creating a new image file may be required, since individual changes made in PS cannot be saved into the LR catalog, but will be saved a a new file, which is then also available in LR.
Many people use LR for almost everything and only use PS for a few things such as pixel-level changes, masking processes, content-aware deleting of objects in the image, and soft-proofing, among others.
From what I understand from some top pros, BB is excellent for QUICKLY doing initial culling edits, and they say that lightroom is much slower for this, but if you find this to be true, you could keep BB and do your initial edits there, then "import" your images into LR to start the cataloging, processing, and database managing of your images.
One more thing I want to say. One of the biggest advantages I get from using LR is the ability to "store"/keep/access/find as many versions of an image as I want with different processing, cropping, and aspect ratios, all from a single image. I hate having 10 or 20 different TIFFs in a folder that are all different versions of the same original image. It drives me mad! (used to) On the other side of the coin, if you take many images of the same thing, but would like to store them in a stack, where you only see one of them until you are ready to process the individual images, you can stack them, then after processing them you can put them back in the stack. This allows you to breeze through and browse your images using considerably less screen real estate.
So, there you have it. I reiterate, though, that it could take more time than you are willing to spend to convert your workflow, only to possibly find little benefit. It HIGHLY depends on what you do with your images once you take them, process them, and go in to the next day's shoot. I think watching the video will give you the insights you need to make the decision.
Take care, and good look with your decision.