Hi @Nova_Espero,
Another great question! 
I hope you don’t mind that I rehomed it into a post of its own- sometimes things can get buried in the comments on other posts. Hopefully, this will help your question get the attention (and answers!) it deserves 
While there may be some practitioners out there who do a full ritual bath cleansing before every spell, I think it’s safe to say that the majority do not (I know I certainly don’t!). So I can attest that spells can work successfully without a ritual bath- in other words, it is not required.
That being said, if you do feel called to cleanse yourself/your tools/your space prior to spellwork but a ritual bath isn’t the best option, there are other ways you could do a cleansing pre-spellwork if you so choose!
This article is focused on cleansing to remove negativity, but the methods it talks about are popular methods of cleansing that would work to simply “touch up” your space and tools prior to spellwork.
The methods here would all work in place of a ritual bath- I’d recommend experimenting to find what works best for you! 
Sorry to hear about your hair troubles- the summer can be really brutal on our hair! I have very thin hair and it tends to get much more oily and gross in the summer 
I’ve found I have to use a bit more shampoo and wash my face/hairline more often- it seems to do the trick.
May I ask if you have experimented with different shampoos to try and find one that your hair might like a bit more? Maybe explore some herbal shampoos?
I was working with homemade nettle shampoo for a while (there’s a post about it here) and it seemed to be working nicely- but I moved back to the US (and away from the nettle) so I’m not sure when I’ll be able to try it again 
I hope you can find what works best for you- both for cleansing and for your hair!
Blessed be! 