It's actually easy to work out. To convert from bit > byte you divide by 8 (since there's 8 bits in a byte). So if you have a 384kbps connection you'd be able to get a maximum of 384 / 8 = 48KB/s, however, it's best to take protocol overhead into consideration. A good rule of thumb to go by is to use 90% of the theoretical maximum speed. So in this case 48 x 0.9 = 43.2KB/s.
So on a good day you'd get between 43 and 48KB/s on a 384kbps connection, but it would be more towards the 43KB/s side of things.