I think you are looking at this problem a bit ass-backwards. As a general premise, in an educational context, there is nothing inherently offensive about letting someone know that their English is poor, if their English is poor. Rather than starting with the premise that this might be perceived as bullying or harassment, start with the premise that it is a valid educational diagnosis, and think about when it is a good idea to raise this, and the best way to deliver this diagnosis and corresponding instructions.
University students in an English-speaking university are learning both the subject matter of their degree program, and the language of instruction. It is perfectly appropriate for lecturers to assist them with both of these things, and this assistance ought to include honest diagnosis of their present level of ability in both. You will need to exercise discretion for how often you think it is useful to raise issues of English competence, bearing in mind that learning a language takes time and practice. In any case, in situations where a diagnosis is appropriate, there are certainly ways you can have these conversations that take the "sting" out of them, just as you can with subject-matter discussions in technical disciplines. However, the desirability of softening the blow from a diagnosis does not over-ride the importance of communicating that diagnosis in an honest and measured way.
In my own experience, students for whom English is a second language ---who have not yet become fluent--- are usually aware that they are not yet fluent. It should be possible for you to communicate the fact that their English is at a level where they can communicate, and you can understand what they are saying, but it has problems in composition, spelling, etc. Most universities have some kind of Language Centre with specialists in English-language teaching, so if your university has one of these, you can refer students there for a diagnostic assessment or for broader assistance. (These centres are also useful for students for whom English is a first language, who nevertheless have abominable composition and grammar).
I have also noticed that this problem is far from being limited to ESL students. I have had many experiences lecturing where the quality of English writing from non-ESL students was extremely poor. (I would say it is "shockingly bad" but I am actually quite used to it by now.) The same basic principles of diagnosis and instruction apply in this case. (And if you think it might be insulting to an ESL student to be told that their English is poor, just bear a thought for non-ESL students who are told that their competence in their first language is poor!)
In terms of the specifics of how to communicate this matter, it is a good idea to think how you can "soften" the adverse diagnosis, but you shouldn't go so far as to mislead the student about their present abilities. Consequently, I think your gut feeling of what to say is wrong in the other direction from which you are worried --- i.e., if the student does not, in fact, have "very good English", you should not blow smoke up their ass by telling them they do. Simply let them know that their English is clear enough to get across their ideas in a basic fashion, but they need to improve their composition, spelling, and grammar. You can then go into details on specific problems you noticed, and also refer them to the Language Centre at your university.
Now, in our especially sensitive age, it is perhaps possible that a student might take such offence to this that they accuse you of "bullying" or "harassment". Neither charge is likely to have any serious merit in an educational context, where your job is to diagnose skill deficiencies and assist students to remedy these. If such an unpleasant thing happens, I recommend you cease one-on-one instuction to the student, seek an alternative lecturer to instruct them in those matters, and proceed with the complaint with the expectation that the university will back you against a non-meritorious allegation. Contrary to what some people seem to think, the concepts of bullying and harassment do actually have some substantive meaning in workplace law and university policy, and they do not encompass everything that a person subjectively perceives as bullying and harrassment.
Finally, I will just note that English is a difficult language, in part because it is huge, it gradually absorbs words from other languages, and it has a substantial number of idioms (e.g., bite me in the ass, ass-backwards, blow smoke up their ass). Fluent English-speakers tend to use idioms commonly without realising it, and for people still learning the language, if they haven't heard these expressions before they can sound very strange indeed.