I think if you go with something like adore violet gem (which is a very pink based purple) you'll get a nice bright purple. Your base is too dark for light/pastel shades but I think you just need to go over what you have with another dye to get a bright colour.
I think you just need to use a better purple, a well pigmented brand such as Special Effects, Pravana or Adore will cover that base.
If you want a prettier fade, or a lighter shade of purple then having a lighter base will help. The better purples will last a lot longer though.
It was definitely a mistake to buy the colours I brought, I was too impatient. Should have ordered from beeunique 🙁
Would I be able to do another bleach bath with this colour on?
You can bleach over the colour, it won't prevent it lifting BUT (and its a big but lol) many purples go green when bleached, the stronger the purple the brighter the green. It looks quite pinky so my guess it will bleach out pink but definitely do a strand test first. The only other issue is it is hard to see how much lift you are getting when bleaching over colour, so if you can fade it first it will make life easier.
My natural haircolor is darker than your hair and when I dyed it purple I got a rich purple colour. I guess it's really a matter of which dye you are using...