To send money from one character to another, you can just mail some coin to that character (assuming they are aligned with the same city). There are mailboxes in each racial village/starting city (usually somewhere near the inn). It usually takes about 30 minutes for the mail to arrive, sometimes less sometimes more.
And you are right about the shared bank slots, however be aware that the characters must also be aligned with the same city. So if you have one toon from Qeynos and one toon from Freeport, they cannot share bank slots.