We were given a bassinet which needed a new customised mattress which we got cut at Clark Rubber but they don’t do mattress covers. Do I need to find a mattress cover before I put on a mattress protector or is this the same thing?

Red Nose recommends that a mattress is firm, clean, well-fitting & flat. (cot or bassinet)
A bassinet mattress should be no thicker than 75mm.
A mattress protector is fine, as long as it is not padded & fits in a way that it is tight (cannot come loose)

Product Safety (ACCC) develops & monitors safety of all products in Australia. They do have some
recommendations (Buying Tips) for bassinets.

Check to see if the bassinet you have meets these safety recommendations.

Ensure the sides of the bassinette are at least 300 mm higher than the top of the mattress base.
Ensure it has a wide stable base and a sturdy bottom so that it won’t tip over.
Ensure the mattress fits well and is firm, smooth and no more than 75 mm thick.
If the product has folding legs, make sure it cannot accidentally fold during use.
https://www.productsafety.gov.au/products/babies-kids/kids-furniture/bassinettes

Red Nose also has the following information about bassinets & buying second hand products.

https://rednose.org.au/article/second-hand-nursery-furniture
https://rednose.org.au/article/bassinettes
https://rednose.org.au/article/baby-safe-sleeping-products