Sometimes when an animal goes lame and there is no obvios sign of a fracture, it is sometimes best to provide anti-inflammatory pain relief as the pain may just be soft tissue i.e. a pulled muscle, tendon, ligament.
If there is no obvious sign of a breakage then, in my opinion, providing pain relief and waiting to see what happens would be the preferred treatment. There is no point rushing in to risk an anaesthetic (esp in such a young bun) if all it needs is a few days rest.
The vet you saw was right - if your rabbit has broken a tiny bone in her toe, for example, then there would be nothing to do but leave it to heal itself. I work in an orthopaedic vets and in such a small animal it would be impossible to pin a toe and even bandaging/splinting can cause more harm than good. A decent supportive dressing would actually weigh quite a lot, so for a baby rabbit to carry around, can end up causing injury and not actually llowing the broken bone to heal. Plus, if the toe is not put into a perfect position, you could end up with the fracture heling in the 'wrong place' anyway. I realise that the bone could heal awkwardly without a dressing, but if its a toe, it is unlikely to cause any major problems.
If the actual leg bone is broken and required pinning, this would have been quite obvious to the vet. However, some fractures can go undetected so i would think that if your bunny is showing no signs of improvement by monday, take him back and they would need to xray in case he does have a break.
If they were to find a break, the treatment would depend on the type of fracture, the bone affected and where in the bone the fracture is. Some breaks are best left to heal, some are bandaged whilst others are pinned or plated. If your not happy with the level of knowledge at your vets, maybe go for a second opinion. If you were to have xrays etc at your vets and then you weren't happy with the treatment they want to provide, you could always take the xrays to another vets for a second opinion.
Hope that helps.
ps - as mentioned previously, repairing a fractured leg is costly. My vets is in surrey and we would charge around £800 - £1000 or so for a fracture repair!! Liverpool should be cheaper than that though.