It depends what the construction of the bedroom walls is, of course (and the scale of the problem, and how much space you're willing to lose off the room).
Assuming they are stud walls, then the minimum would be to fill them with something like Knauf Earthwool Acoustic mineral wool insulation (this will reduce the transmission of higher frequency sounds).
Next step would be to use a couple of layers of Gyproc Soundbloc acoustic (high density) plasterboard, fixed with the sheets staggered. This adds mass to the wall, and reduces the transmission of lower frequency sounds.
As you've already identified yourself, that then leaves the problem of flanking transmission via the floors.
Without going into too much detail, best I can do here is point you in the direction of the Robust Details Handbook (Google it: you need to register with your email address, but can then download it free of charge). This has plenty of solutions for floor and ceiling treatments, but also take note of the details they use to isolate wall-floor junctions... one of the main ways to prevent flanking sound transmission is to introduce discontinuities, so for example the plasterboard on the walls should not directly contact the floor deck, but should be sealed and isolated from it using resilient strips.
Also download and read through Approved Document E to the Building Regulations, which similarly covers a lot of the basic principles and solutions.
As I said, it all depends what the scale of the problem is - whether you just casually want to minimise sound transmission where it is possible and easy to do so, or whether there's a serious and definite issue to be addressed - but, like airtightness on buildings, a lot of it comes down to attention to detail and workmanship if you want to go that extra mile.