We are discussing the catenative verb don't want in a complex construction with a gerund-participial. The subject of the catenative verb is you and its object is the non-finite clause a hungry bear or other animal suddenly appearing in your tent, where the NP a hungry bear or other animal is the agent of the verb in gerund appearing. "Want" in the affirmative is generally said to be followed by a "to infinitive" (except for the concealed passives of the kitchen wants painting type). Even in the negative, if the subject of "want" is the same as the agent of the verb of the object clause, the to infinitive will be used ("I don't want to leave"). So it is good to narrow the issue you are raising to the particular instance of non-affirmative catenative "want" followed by an object clause where the agent of the verb is different from the subject of "want".
In theory, the difference in meaning between I don't want you doing and I don't want you to do is negligible. I found a short reference to the use of gerund-participials after want and don't want in Rodney Huddleston & Geoffrey K. Pullum (The Cambridge Grammar of the English Language, pp. 1231-1232):
The gerund-participial with want generally has a progressive
interpretation, but in non-affirmative contexts it can be
- I want them standing when the Minister enters
is equivalent to
- I want them to be standing when the Minister enters,
contrasting with non-progressive
- I want them to stand when the Minister enters.
- I don't want you bringing your dog with you,
the meaning is to bring, not to be bringing.
However, almost 20 years passed since that grammar was published and anyway it was only concerned with the progressive or non-progressive nuance of the meaning. Gerunds have seen an increase in use, and although it is difficult to find more exhaustive explanations on this issue, I think people in their conscience may have begun to give it a slight nuance. In your context, it looks like the author of the statement explains generally a situation in which this sudden turning up of the bear might happen every time the situation is repeated. So
You don't want a hungry bear or other animal suddenly appearing in your tent [every time you leave bits of food on the ground or keep unused food in open containers in the camp].
The author may have felt that
You don't want a hungry bear or other animal to suddenly appear in your tent.
is more punctual, for one particular situation, rather than for repeated instances of the same circumstances.
In support of that, I found this post of a native English speaker:
Go for the gerund, if you want to stress repeated action: "I don't want you coming home so late". I don't want you to come home so late,(using the infinitive), is more likely to infer the action happening once, or occasionally, of course depending on the context. (WordRef)
Here is another thread that agrees with the two nuances:
There's usually no difference intended in sentences like this, but here are a few comments on nuances. "I didn't want anyone thinking I was trying to be a pet of the teacher" sounds a bit like the 'anyone' might be thinking this for a long time. I didn't want that. "I didn't want anyone to think I was trying to be a pet of the teacher" sounds a bit like maybe the 'anyone' might just think this briefly.
Another post from an MA Linguistics says:
The nuance is slightly different.
“I don’t want you to do that” has the slight implication that you
haven’t done it before. Mother says to child, “I brought some chips
home, but I don’t want you to eat them.”
“I don’t want you doing that” implies that you were caught in the act
of doing it, or have been in the habit of doing it. Mother says to
child, “That’s the third time all the chips have disappeared! I don’t
want you eating those chips!”
But it’s just a slight nuance. Really, either form could be used in
This last post adds another slightly different nuance, that of habit, but the emphasis on repetitiveness conveyed by the gerund-participial and non-repetitiveness conveyed by the to infinitive is obvious. It could point to the habit that bears have of coming near humans when they smell food.