To buy bitcoin with bank accountmeans that you want to enter into the bitcoin network. You will have to be careful so that you protect your privacy while on the network. The following are ways in which you can achieve that.
Take care while in public spaces
Unless you have an intention of receiving full transparency payments or public donations, using a bitcoin address while on a public space like social network or website might not be a good idea as far as privacy is concerned.
If you happen to do so, then know that, in case you happen to move your funds with the address to other addresses that you own, they will automatically be tainted by your public address history. You might want to be careful to avoid publishing information about purchases and transactions that might allow someone to get to know your bitcoin address.
It is possible for your IP address to be logged in
Because the network for bitcoin is the peer to peer type, it is possible to get transaction relays and listen to them and log onto the IP. It means that, to find where a particular transaction came from can be hard and bitcoin node of any kind, can be mistaken to be a transaction source when in actual sense, they are not. It might be wise to hide your computer IP address so that it will be hard to be logged in.
Limitation of mixing services
Mixing services are online services that offer traceability that is mixed between different users through sending and receiving back equal amount through buy bitcoin with venmo addresses. You have to remember that, the legality of utilizing a service like this one might vary depending on your jurisdiction rules. You will need to trust the individual who is running such services not to steal or lose your funds or keep your requests log with themselves.