We need to understand the meaning of the French. Since opinions about what seems natural have degenerated into a spitting contest, let's look at some external resources rather than just say "what sounds right to me". The following examples were found in several different reliable resources:
- passer une nuit à l'hôtel = to spend a night at a hotel (Oxford French Dictionary)
- passer du temps = to spend time http://www.wordreference.com/fren/passer%20du%20temps
- je passe mon temps à lire = I spend my time reading https://www.larousse.fr/dictionnaires/francais-anglais/temps/76325
The interpretation of "spend time" and "pass time" are perhaps more context sensitive. Are we focusing on using "pass" because of the French verb "passer"? That doesn't make it more correct. Resources aside, people do say both "spend time (with)" and "pass time with" and it seems that those in one camp cannot abide the other. Both expressions are accepted here but we are reminded that BrE and AmE may have a different sense of what sounds natural. Please accept that others have different preferences.
I think a large part of the fixation on "pass the time" is because the suggested solution on Desktop if you enter "I like to pass the time with her" is "I like to pass some time with her.," which is a relatively awkward construction (at least in American English). If I heard someone say that, I'd assume they were messing up the idiomatic phrase "pass the time." From what I can tell, "spend time" is probably the most accurate translation, and it might be prudent to remove "pass some time" from the acceptable list of answers unless the phrase is used in some other dialect of English.
The reason why 'j'aime' is to be translated as 'I like' is because the "thing" being liked/loved is neither a person nor a pet. Instead, the thing that the speaker likes to spend is time. The qualifier 'avec elle' is merely added as a way of telling us about how/where/with whom the speaker likes to spend his/her time.
According to the Cambridge English Dictionary the definition of "pass the time" is "to do something to keep busy while waiting" eg - "we passed the time in the airport playing cards" which is slightly different in meaning to "to spend time" which is what I understand the french to mean.