Western Union is best for transfers, $1.99 charge if using account debit card, $4.99 if transferring direct from account. Debit transfer is instant, from account takes a couple days. Their limit is $30,000usd. Not sure why any bank would put a limit on a deposit.
I’ve always used WU to transfer funds to BB, I use my debit card for WU to access funds, regular cost is $1.99, each transfer gives you bonus points to reduce the cost, my current cost is $.99. On my last transfer I got a screen that said more information was required. I had to upload a photo of my passport page and also take a live photo of myself, describe source of funds (income) and reason for transfer (family support, living expenses), those choices were from a drop down menu. The funds were in my BB account within seconds of exiting WU app.