It sounds like you acted quickly and correctly in removing the mushy bulb so that was good and of course the new growth is good. Do you have a good Oncidium culture sheet? If not check out the orchid care section of this forum or visit
AOS | Home and look at their culture sheets. From this point on it sounds like good culture is all you need and your orchid should do fine.
Digitalgate, are you talking about another genus, Dendrobium perhaps? Oncidiums don't keiki.