Doing a culture is of course ideal before starting a pet on antibiotics, but there are several warnings with a culture. 1) it is a very pricey thing to do and probably is not necessary in most cases of 'routine infection'; 2) it takes at least 4 days minimum to get results that will help you pick the proper antibiotic, and waiting 4 days may not be in your pet's best interest, but 3) most importantly, what are you going to culture when dealing with a possible nasal discharge/infection? The discharge? the nares? The mouth? The lungs? Ideally you should be culturing the deep sinuses where, if there is an infection, the bugs are living... how do you get them? There simply is no way to realistically culutre upper respiratory bugs short of surgically opening your pet's skull and getting to the 'root' of the problem (something I would not normally recommend). Culturing anything else, such as nasal discharge, the nares, the mouth etc. is only going to probably result in growing a lot of incidental bacteria which may or may not have anything to do with the infection.
So if someone offers you a culture for whatever infection your pet may have, ask how they are going to get it, what material they are actually going to culture, and then think about whether that makes any sense. For example, for a possible urinary tract infection, culturing the urine (steriliy) is what needs to be done... and THAT makes sense. But when dealing with respiratory tract infections, it is the respiratory tissues that should be cultured.. .but they very hard to get to (not impossible, but nearly)... for lung infections, we recommend what is called tracheal washes, which are not super easy to do in bunnies, but can be done and often give you the actual bug you need. But as I explained above, upper respiratory tract infections are very hard to culture without getting a lot of other bugs that are NOT causing the problem... makes interpretting the results difficult. And MOST (95%) of all upper respiratory rabbit infections are one of two bugs (Staph or Pasteurella, with the other 20 or so possibilities being way down on the list).
So if your vet does NOT offer you a culture for this problem (which actually doesn't even sound like an infection from your description), then don't think he or she is doing bad medicine. They are just being realistic.