Bluetooth has latency.
Really, I would go up to the $100-$200 range for headphones. There are some great options around the $150 mark that would be better that cheaper alternatives. I have Audio Technica and Beyerdynamic headphones in that range that work and sound great. I have a few cheaper pairs I use when I need to record a disrespectful turd that can't hang my headphones up after a take, and there is a noticeable difference. It works like a punishment at that point. If my headphones end up on the floor, you get to use the cheap shit. I just wish they came in pink.
If you get closed back, they block out the surroundings better and isolate better for tracking. If you don't need to isolate or worry about headphone bleed into a microphone, get some open back headphones. The Beyerdynamic DT 990s are great open back headphones that sound really natural.