I will assume that whatever Alice did to startle Bob was a breach of a duty that she owed to Bob, in order to get to what I see as the more interesting aspect of the question: whether Bob's intervening act removes Alice's liability for the breaking of the television. There are certainly scenarios where Alice might have startled Bob without even breaching a duty, but in that case the analysis would end there.
A startle reaction will almost never sever the chain of legal causation
In negligence, Alice is held liable for harm that is reasonably foreseeable as a result of Alice's breach of a duty. One of the elements of a successful negligence claim is causation: Alice is not liable for harm that is too remote from her breach.
On its own, proof by an injured plaintiff that a defendant was negligent does not make that defendant liable for the loss. The plaintiff must also establish that the defendant’s negligence (breach of the standard of care) caused the injury. That link is causation.1
(Clements v. Clements, 2012 SCC 32, paragraph 6)
Bob's startle response would almost certainly be considered a foreseeable reaction, and thus, not sufficient to separate Alice from the breaking of the television.
An instinctive human reaction, or any non-negligent human action in the chain of causation will almost never break the chain of causation, because such reactions will be held foreseeable; and even if they are not, the precise chain of events leading to an accident need not be foreseeable.
(Ken Cooper‑Stephenson, Personal Injury Damages in Canada (Carswell, 1996))
See also The Restatement of Torts (Second), § 447, which says that an intervening act does not remove the defendant's liability if: "(a) the actor at the time of his negligent conduct should have realized that a third person might so act, or (b) a reasonable man knowing the situation existing when the act of the third person was done would not regard it as highly extraordinary that the third person had so acted, or (c) the intervening act is a normal consequence of a situation created by the actor's conduct and the manner in which it is done is not extraordinarily negligent."
"[I]t is the general nature of the intervening acts and the accompanying risk of harm that needs to be reasonably foreseeable. Legal causation does not require that the accused must objectively foresee the precise future consequences of their conduct." (R. v. Maybin, 2012 SCC 24).
Foreseeability does not require that the intervening action be probable; it only requires that it would not be brushed aside as "far-fetched."
The degree of probability that would satisfy the reasonable foreseeability requirement was described in The Wagon Mound (No. 2) as a "real risk", i.e. "one which would occur to the mind of a reasonable man in the position of the defendan[t] ... and which he would not brush aside as far-fetched"
(Mustapha v. Culligan of Canada Ltd., 2008 SCC 27, paragraph 13).
Examples of intervening acts held to be reasonably foreseeable:
- Haynes v. Harwood  1 K.B. 146. A carriage owner had left a two-horse carriage unattended on a busy street. The judge accepted evidence from an independent observer that two boys had come along and one of them threw a stone at the horses and the horses bolted along the street (these boys were not before the court as co-defendants; nothing more is said of them). A constable managed to stop the horses, but was injured in the process. The carriage owner was liable in negligence: a reasonable person should have foreseen that the horses might get loose and someone be injured while trying to stop them. The court said, "it is not necessary to show that this particular accident and this particular damage were probable; it is sufficient if the accident is of a class that might well be anticipated as one of the reasonable and probable results of the wrongful act."
Foreseeability here does not have its colloquial meaning
Greendrake's answer says that "whereas Bob's shock is foreseeable, I pretty much doubt that him breaking the TV is." In my view, this takes too colloquial a view of foreseeability. As Hart and Honoré say in Causation in the Law, 2nd Ed. (1985):
... in one sense everything is foreseeable, in another nothing. The consequences of negligence are almost invariably surprises. All depends on the detail with which the harm is described. ... there will always be some details of the recoverable harm which are not foreseeable.
... the fact that harm described by reference to certain details is not foreseeable does not render the harm, more broadly described, unforeseeable. ... If we have learned from experience to expect a 'rainstorm' on seeing dark clouds, then the rainstorm was foreseeable even if, when it occurs, it has other characteristics (e.g. lasted two hours, covered an area of 40 sq. miles) which we could not foresee but which might appear, ex post facto, in a more specific description of it.
Of course, foreseeability is a question of fact, and I acknowledge that a finder of fact might very well conclude that swinging a vacuum is not within a class of actions that might be anticipated by a reasonable person. While I disagree with Greendrake's analysis and conclusion, the contrast with my answer helps highlight precisely where the issue would be if this were to be litigated.
1. Note the terminology. The breach of the standard of care is the negligence. But liability only follows when the negligence causes harm. This is contrary to the framing in Dale M's answer, which says, "Alice was negligent if her actions caused damage to Bob’s TV," and that "[i]f we are talking about Alice’s TV then there is no negligence because Bob has suffered no damage." That language conflates negligence (the breach) with liability (breach plus causation).