Resistor completely blown, how do I found out what to replace it with?

The fact that it was a ceramic is a clue that it was a power resistor.

The size (length x diamter) is another that will tell you the wattage.

The construction inside is either carbon or wirewound.

Carbon are low inductance and wirewound are very stable and accurate.

The ohmage is probably smaller than 100 ohms since speakers are generally 8, 4, or 2 ohms.

Unless you can provide a brand for the speaker and where is was connected across it is difficult to know. You would need to contact the manufacturer of the cabinet (if the speaker came with the cabinet) or the speaker manufacturer (if mounted as part of the speaker).

But a better way would be if you have another speaker and look at the color bands or markings on it and report it back here.

From there i can find you a part to buy and where.

There is no way to tell except for getting a copy of the schematic diagram or call the manufacturer, If it is from a simple bass cab, it probably is an eight ohm power resistor.