The most important question is whether anyone else should be a coauthor. From your description, it's unclear whether the professor you were initially talking with should be one (the others do not sound like coauthors at this point). The fact that you describe it as "completing a paper that I had started with initial discussions with a professor" suggests that maybe he should be. The key issue is whether he contributed anything significant to the paper's content. If so, then you need to discuss the authorship issue with him and cannot make a unilateral decision. If he did not contribute anything, then there is no ethical barrier to submitting the paper to the arXiv or a journal if you choose to do so. However, you should be careful with this decision, since it is a major problem if the two of you disagree about coauthorship (especially if you find out after you have already submitted the paper without him). If you think the situation might be ambiguous, then you need to discuss it with him before submission.
When I say there would be no ethical barrier to submission if you have no coauthor, I mean submitting it would not be a form of academic dishonesty. You might still offend people, if they feel you are not taking their advice seriously or giving them a sufficient chance to respond. I'd recommend giving everyone plenty of warning before submitting the paper. For example, you could send an e-mail saying something along the lines of "I'm just about done with the paper on topic X. I'm planning to submit it for publication in a month, after I do some final polishing, and I would greatly appreciate any feedback or suggestions you may have." (But don't say it this way unless you are sure nobody else could have a case to be a coauthor.)