Hi there, first order of business is to check the skin-safe usage rate of each individual oil, or blend of oils, on EOCalc.com. Some EOs like lavender are very skin-safe and can be used in higher amounts. Others (cinnamon, nutmeg, thyme, oregano) are "hot" oils and have to be very, very diluted, or not used at all.
I would purchase the plain EOs, not in carrier oils. You will want to get them from a soap or candle supplier since you will need a lot of each EO. Don't be fooled by MLMs that tell you only theirs is "pure." There are only so many EO suppliers in the world, and all reputable sellers purchase from the same small group of quality suppliers. Plus, no one can afford to use MLM EOs to scent their body care products. I don't know which suppliers are available in your area, but not doubt some of the other Aussie members will be along shortly to help with that. @Relle
You will also want to use polysorbate 80 or another solubilizer to ensure that your oils are well-dispersed in the bath bomb mix and then the bath water. I recently read that some folks are using a bit of liquid soap as as less expensive and less stinky solubilizer than PS80, but I haven't had a chance to test how well it actually works.