The Bing and Google algorithms are not identical, so it’s not accurate to say that ranking well on one will automatically lead to ranking well on the other. You can try using this tool to check your ranking. Basically, you just copy/paste your URL, and then Bing’s SEO Analyzer will provide you with relevant data and suggestions on how to improve your ranking.
Also, Bing is a lot more reliant on social signals than Google, meaning that doing well on social media is incredibly important for your overall ranking. So, it’s essential to be active on your socials and utilize all the marketing advantages that different social media platforms offer.