Besides that, I think that if you use the banks to send the money to the other site, it will need a long time before the money can arrive at them so they can proceed with your transaction. But you can try for yourself, so you will know how long it will be needed to buying bitcoin from your bank account to another site.
You can reply to your bank by asking what is the purpose to keep my money in local currency. On top of that, they don't have to patronize people to say what to buy or not.
Your second point is totally wrong, I suppose you never used a bank transfer to an exchange. It takes 2-3 days max, often 24 hours. If I make a bank transfer to kraken right now (it's 2.00pm here) It will hit my Kraken account tomorrow morning.