It really depends on your horse's metabolism and level of pain, so you kind of have to "experiment" and make a note about how your horse reacts. Then remember that they can also grow tolerant to the drugs when they are used for long periods.
In my experience, oral paste usually shows results in 1-2 hours with effects lasting 12-24 hours. IV will show results in about 10 minutes. (I hope you aren't doing any IV injections without knowing how to properly give it though) Liquid bute must be stored in the fridge and can ONLY be injected IV NOT IM. You can however, save a little money and time for a horse who spits out paste or foams up & drools it out by giving the liquid dose orally. Again, that would take about an hour or so to see an effect. Pills take longer to show results.
I personally prefer Equioxx or Banamine over Bute though.
Has your vet advised you to bute her before riding? I only ask because doing so prior to a ride will cover up anything that is going on and potentially hurt her more. Personally, I would pony her a few times (if you haven't already) walking and trotting to see how the legs hold up and then give an NSAID and more rest if she shows signs of trouble. Splints are relatively minor injury and heal pretty well and fast as long as they get rested and don't go back to strenuous activity right away. If your vet said to do flat work, by all means, do it, but I don't know if it is a good idea to give pain drugs until you actually know there is pain. You don't want to further her injury by letting her feel too good.