If someone is in my way of accomplishing something, or I have competition in a certain situation. Could I use a binding spell to banish them from being in my way? Would it bring me any type of bad karma?
Most times, in my experience, if one has to ask if something would give negative karma, it probably is going too. As a rule of thumb, anything that is overly forceful or unnecessary might do so, in a minor manner.
I would have to look at the exact specifications of the binding spell in question to fully answer that, but based on what I know of them, such a spell may not work unless you are wanting to drive them to somewhere you already want them to go. If it's something they do not want nor ask for, it's entirely possible that it will not work, cause undue suffering, to you and/or to them, and cause negative karma to yourself. A combination of the three is likely to result.
I recommend instead of trying to find a spell to remove obstacles, that you confront them directly. Not harshly, but positively. Let these things know what you desire and express your energy in the calmest way possible. It will leave the ball in their court, as well as the consequences of their own actions.
If you still feel the need for divine intervention on your path, look up on information on Ganesha. Get to know that deity, for one of his major attributes is being the Hindu God of Removing Obstacles. Be careful with that desire though, he may see things in your way you do not consider obstacles, but are best removed for your potential growth.
You could bind them from causing harm or getting in your way, and it should not cause any kind of bad mojo if that is what you mean.
Be specific in your binding. You do not want to cause them any trouble in their life. So be clear that you are only binding them from effecting you.
You could use a simple rope binding. But a good one I thought of recently is an ivy binding. Ivy is an interesting plant. It can block out all light and suffocate any plants in its way, or hold them in the light helping them to grow even more healthy than before. I would take a picture of the person in question, and bind them into a healthier path out of your way visualizing ivy supporting and holding them. Just an idea. Once again make sure your intent is clear and you should be fine.