It doesn't even need the bull run for BNB to recover back to $310 because when Bitcoin was around $31k, the price of BNB was above that range, so all it needs is Bitcoin to recover from the current range and go back near its previous resistance which was $31k and then we will see BNB recovering the desired price by OP. For the bull run, we would obviously expect BNB to show some magic and maybe go around $1k if Bitcoin manages to go across it's previous all-time high.
Bnb prices down after SEC issue happens in june 2023 and from that time we have seen constantly decrease in price. First price dump to 250$ and now further dumps to 210$. I think you have not seen the chart, previously when btc price was above 31k bnb was trading around 260$ so OP is right that only bull market could bring price back to 310$.
XRP
BTC
Above $1k is my target price for BNB in the bull run because it went around $686 last time when Bitcoin went to $69k, and if Bitcoin manages to hit $90k or more this time around, we should probably see BNB performing as well as long as Binance stays clear and there aren't any issues at that time.
You are hoping so much high price, 1k$ is not looking to be reached even if btc reaches 90k$. crypto market not works according to previous data. Other factor also impact the price of coin. The XRP example is front of us. BNB is now under eye of the SEC and no one will take freely risk in this coin so t think 300-400 $ could only be expected in this situation.