Your problem appears to be one of communication. I would suggest trying to work through the problem with your coworker if you can first. The reality is that even once this problem is "resolved" you two are still going to be enemies, and it will occur again and again.
That, however, is a separate question altogether. I suggest you ask that, or search for how to improve relationships with coworkers.
On to the problem at hand:
What steps should someone take when reporting their bullying issue to management isn't taken seriously?
Again, this is an issue of communication. Your company may have rules against eating at your desk. You should ask your manager to clarify the rules since you were unaware of them. Ask for the rule in writing, so you don't misunderstand them. If they don't exist in writing, keep that information for future use.
Your company may have rules regarding personal use of fragrances or aerosols. Ask for clarification about what rules the coworker was operating under when she sprayed your work area with an offensive perfume that ruined your lunch.
Now ask what rules the company has about gift giving and gift returns. Make sure they understand that you are asking these questions in order to make sure you are in compliance.
Then you need to find out the companies bullying response policy.
Now review all the relevant rules, and determine which ones you broke. Then spend some time writing a letter apologizing for those rules you broke, explaining you were unaware of them at the time, and that you will endeavor to fulfill them in the future. If you want to pursue the lunch spraying incident ask how the rules permit employees to spray other work areas, and if you are also allowed to spray her work area if you find her perfume, coffee, or body odor aggravating. Make sure they understand that by allowing this woman to spray you without discussing the problem first, she is in direct violation of the bullying policy as described.
Then continue the letter explaining how the whole process unfolded, and how much you were hurt at specific points of the process. Emphasize that it's not about the lost lunch and disrespectful coworker, but what concerns you now is that your concerns were not treated appropriately by management and HR. Point out specifically where their response is in direct violation of the bullying policy as explained.
It is by likely that once you present them with written letter or email, they will backtrack significantly. Written words that leave a trail of vide cue get more action than verbal discussions.
But it's clear that these issues are aggravated by your lack of communication, or style of communication, with your coworkers. I believe you can resolve these issues much more quickly and painlessly if you work on your interpersonal skills. There are many, many books on the topic.