I am sorry that you have been waiting for a response. I recently just logged onto the site and noted that your question hasn't yet been answered. I am a licensed veterinarian with over 25 years’ experience and would be happy to work with you if you are still needing assistance.
In answer to your question about can this wait or not, it is not considered an emergency and now that the salivary cyst has ruptured, the pressure is released and the inflammation should start to come down. They most likely have her on antibiotics as well and hopefully something for pain. Giving it a little time to let the inflammation resolves some will likely make the surgery a little easier as long as it is certain side has the cyst.
Here is a link with a little more information about this LINK HERE
It is not possible to comment on the recovery time of this as I cannot evaluate to what degree the site of the ruptured cyst is inflammed or infected and we don't know what caused the rupture as of yet. In many cases, it was simply an occlusion of the salivary gland or duct, for some reason, but if there as an underlying cause, like a mass, that may change the procedure. Surgical removal of the salivary glands on the affected side is the usual treatment and in the hands of an experienced surgeon, that is not a complicated procedure, but depending on the degree of tissue damage due to the rupture it could lead to complications. I would estimate that in an uncomplicated procedure, recovery may be about a few days to a week, but hers may be longer, especially if drains need to be placed for a few days.
I hope this is helpful. Please let me know if you have ANY other questions. My goal is to give you 100% satisfaction and if you are not yet satisfied, please reply so I can clarify for you.