Is there a mobile app that I can use to buy/sell bit coins? Would it be useful if I create one?
There is a lot of applications allowing you to easily trade bitcoin on your mobile phone. Almost every bigger Bitcoin Exchange has one. Take a look at cex.io, bitfinex.com and many more, they do have mobile apps already. There are also decentralized exchanges with mobile applications too. If you check https://coinmarketcap.com/rankings/exchanges/ you will see a quite comprehensive list of exchanges that we have already.
Another thing is that there is no such thing as an app for trading Bitcoin without having proper infrastructure, the trading engine that can handle large volumes and real-time trading, agreements with banks, special permissions, and licenses so my simple answer would be - no.