Teal to ashy/silver blonde?

Try colour removers first, you'll get a good idea of your Base and then we can help further. You may find under your semi you're blonde already and may just need a toner like Pravana Silver diluted to get you to your required shade. A permanent colour will bleach your hair and then deposit colour but if you're light enough under your semi you may not need to bleach anyway. Hope that makes sense.

So I FINALLY got round to fading my hair as much as I could and have a pastel turquoise-ish colour

How can I make my hair more silvery, preferably without bleaching again? All silver dyes are lilac-ish and intended for blonde colours.

If you put a diluted cool-toned pink on it (I suggest diluting with a silicone-free white conditioner), it will turn purple and should fade to a gray/ silver. Of course do a strand test first to determine how light or dark you need it.

If you aren't already you should definitely start using a purple toning shampoo. I use Clairol Shimmer Lights--you can get it at Sally's or online for about the same price. It will turn your faded teal to a metallic icy blue in one wash. I swear it's magic.