Bubbles may be a machine, but it is not true that you can't have emotion without biology.
Bubbles is also sentient, and you can't have sentience without emotion.
Seriously, there is no sentience unless there is a purpose for which actions are chosen - ie, a sentient creature has a reason to care.
Wittgenstein claimed (correctly IMO) that consciousness is a byproduct of marshalling information for purposeful action. And every part of that statement is meaningful. A nervous system (including brain) is what transforms sensory inputs into motor outputs, in the most efficient way it can to bring about survival and reproduction. That's it. From those 302 neurons in a roundworm, all the way up to us, that's what they're doing. Just that we've found a very different survival strategy, and ours requires a more complicated brain.
The thing is, the roundworm doesn't require sentience. Sensory inputs, including some that detect muscle contraction, are connected directly to muscles, and the whole thing works on reflexes, like an electro-chemical automaton, without the need to marshall information. There are no decisions to make, and therefore no need to organize information to make them, and therefore no need for the roundworm to care about anything in order to give information context for its decisions.
But when you get to brains that actually have to make decisions and deal with unexpected information, there is no context for organizing novel information for those decisions unless there is something that the mind cares about.
Or, TLDR: Accepting that Bubbles is sentient, means accepting that she cares about things and therefore has emotions, regardless of whether she is a machine.