It is not common to send the signal from your amp into a DI box. You certainly don't want to use the speaker out unless you have a high quality DI specifically designed to do so. I believe a countryman and Millenia TD 1 accomodate this but it is not commonly used by bass players for such.
In most cases you will plug your instrument cable directly into the DI box, then run a small cable from the DI box to your amp. A seperate XLR out of the DI box goes directly to the house.
CAPEBASS - many good quality amps with a built in DI have a switch for sending your signal PRE or POST, reading the owners manual will tell you if that signal is before or after the compressor in the signal chain. Depending on your unit a professional may be able to rewire a jumper to change the POST EQ DI to include the compressor.
This all being said and my statement is certainly debatable but most engineers in a live environment want a PRE signal for FOH applications and may insist on an outboard DI for such, yours or their own.