So let's change the situation a little bit. Say we have a Seperatist C-ROC with Corsair Refit and Discord Missiles equipped.

1. Choose to use the bonus attack header from Corsair Refit to perform a missile attack.
2. Look for an equipped missile card to perform an attack with.
3. We don't find one, because Discord Missiles don't have an Attack: header, nor any other attributes of an attack.
4. Ergo, no attack can be made. (We could instead use Corsair Refit to make a cannon or turret attack, if one were equipped.)

Now, let's replace the Discord Missiles with Concussion Missiles, for example. Concussion Missile obviously does have an Attack: header as well as all the other attributes associated with a special weapon.

1. Choose to use the Bonus attack: header from Corsair Refit to perform a missile attack.
2. Look for an equipped missile card to perform an attack with.
3. The only one equipped is Concussion Missile, so that's the one we'll use.
4. In order to determine what to do with it, we have to read the text that follows the Attack: header, otherwise it'd just be a 3-die ordnance attack with no charges or special text. Since that seems rather ludicrous, it stands to reason that we are now 'using' that attack header for the purposes of the once-per-round restriction.
5. Even if we also had an Ordnance Tubes equipped, no other Concussion Missile attack should be possible, because it's already been used this round. If we somehow also had a Homing Missile, for example, equipped, we could totally use Ordnance Tubes to fire that, though.

Coming back to the original question, we equip our C-ROC with Corsair Refit and Cluster Missiles. The attack procedure begins as previously stated; as before, we are obligated to reference the Attack: header on the Cluster Missiles card to know what to do with the attack. It tells us that after this attack , we may perform this attack again with some extra targetting restrictions, etc.

On one hand (argument for only one attack with Cluster Missiles), in order to know what to do with this attack (the second one), we have to again look at the Attack: header... which we have already used. RAW, we don't get to make that second attack because we've already used that Attack: header this round.

On the other hand (argument for up to four attacks with Cluster Missiles), we've referenced the Attack: header and determined all the attributes for the attack, which carry over into the bonus attack granted by the text. We perform this attack and then we perform this attack again as a bonus attack... and now because unlike Standard Ships, Huge Ships don't have a limit to the total number of bonus attacks per round, we have performed this attack (for the second time), which instructs us that we may perform this attack as a bonus attack. As long as we can continue paying the costs (like spending charges) and selecting valid targets, we can continue making bonus attacks.

On the gripping hand (argument for up to two attacks), we read the Attack: header and all of its subsequent text, which goes into the ability queue and resolves one time, generating two attacks as it does so. Both attacks (per the Rules Reference section on Bonus Attacks on p.6) have all the same restrictions and costs except as noted in the text. The kicker is that the text telling us that we're allowed to make a bonus attack afterwards is a seperate sentence from 'Attack: spend 1 charge', so that's why that part isn't carried over into the bonus attack.

In conclusion, I think I've convinced myself that 'two attacks' is the correct answer, and if you've read all of the above without blowing steam out your ears, you probably owe yourself a cookie.