Not bleached long enough? Can I try again?

Can you bleach again, yes, should you bleach again, no, it is always better to wait.
Even if it didn't lighten as much as you'd hoped it will still have damaged your hair, so it is up to you if you are prepared to risk further damage by bleaching again before you have seen the full effect of the first round of bleaching.
I would definitely wait a full week and allow my hair to get really greasy before considering another process just to protect my scalp.
BTW what bleach powder did you use? If your hair is already blonde and you used 20/30 vol for 20 minutes it should have lightened more than it did. I would get a better bleach in the future. I would use 10 vol for 20-30 minutes to take blonde hair up one or two levels.

Thanks for the advice *wicked pixie*

Given the previous excellent condition of my hair, I hope it means it can take a little bit more of a bashing without terrible side effects. 

I'll look into buying some 10 vol bleach online (they only sell 30/40 near me).  I used Jerome Russell high lift powder, a full, new sachet.  The liquid was half Jerome Russell 30 vol and half random 20 vol I bought online.

I'll wait as long as I can (at least the weekend if not longer), invest in some coconut oil and try bleaching for 20-30 minutes more to see if it lightens enough to use a natural blonde/beige blonde toner.  I'm not going for white/peroxide blonde, just trying to get close-ish to my natural colour.

If you just want to remove dye build up, I wouldn't bleach at all. Bleach powder with oils, shampoo and hot water are more effective for fading dye.
Can you post a pic of the current colour?

I did a Head & Shoulders shampoo cap tonight to remove some of the ash blond toner, this has greatly reduced the greenish tinge (particulary on the ends) to a reasonable level. 

My main problem is the too-yellow bleached base, which didn't really tone lighter even with purple toning.  The yellow base shows through quote strongly in reality, though it doesn't look bad at all in pictures taken just now, typical!

It looks pretty ok in artificial light, but daylight is not my best friend at the moment as I look like I'm wearing a cheap yellowy wig 🙁

A more accurate picture taken now in better lighting, really captures some of the wiggyness:

So you want to match the yellowy root colour to the ashy shade on your lengths?
If so, i would try again with the purple toner. either make a stronger mix or leave it on longer.

Sorry if I'm not being clear enough, I want to remove the yellow from all over my hair.

The ash toner made it look a bit green (as it was yellow covered with light brown toner). The yellow all over is too dark to reduce with purple toner. If I make the purple toner any stronger it will come out visibly purple over the yellow - I used to use purple toner a lot when my hair was natural blonde to lighten it so I have some experience with them.

Essentially, I didn't leave the bleach on for long enough, the base didnkt lighten enough and I'm stuck with a too-yellow base that won't tone with purple and so I've temporarily masked it with ash toner that's darker than the yellow base until I can bleach again.

You can tone any colour with the right toner, there is no such thing as too yellow, only too yellow to tone to white if that is your aim.
If you are worried about getting purple hair try building up gradually by using a little violet in every wash.
Getting the toner right is definitely tricky, but also definitely possible. What dyes are you using?

Thanks again for your help and advice.

I'm not aiming for white, just a bit closer to a natural colour, similar to the blonde top colour in my icon (at the moment it looks very fake, yellow and unnatural).  I used some Paravana violet in 'cone free conditioner, left it on for a hour.  It slightly lightened it, but it still looked too yellow and unnatural.

Hello, I would wait four weeks ideally before lightening again so you don't start to get breakage as bleach damage can take weeks to show. Then after I would suggest bonacure silver shampoo for toning, I get mine from Amazon. Superdrug do a cool blonde toner which is also good and cheap! You will probably find you don't need to do too much of a strong bleach and could use 10vol as wicked pixie has said, as you only want to lift one or two levels, so perhaps a bleach bath would be good for you, there's lots of info on bleach baths on here if you need help with that (I can't link on my phone sorry)
Good luck! 🙂

Thanks for the advice *glitterpix*.

I did another shampoo cap with Head and Shoulders tonight, followed by an application of Superdrug 'cool blonde' toner (I realised I had an ancient bottle half full in my bathroom!). It really seemed to make a difference, much more than purple toner did. At this point I'm willing to wait a month to re-bleach as suggested (or bleach bath, I've done those in the past)m

Thanks both for you help and talking me down from bleaching again too fast! Sometims it takes a few days to get used to any change without freaking out!

Thanks both for you help and talking me down from bleaching again too fast! Sometims it takes a few days to get used to any change without freaking out!

This is something I'd like to tattoo backwards on many peoples foreheads. So they see it in the mirror when they first dye their hair! 😉

I waiting (impatiently) for 4 weeks to pass, then decided to use Belle Colour in Extra Light Ash Blonde (30 mins processing time). 

Thrilled with the outcome, took me pretty much back to my natural light ash blonde and the condition of my hair has felt much better post colouring - post-bleaching it felt strawlike when wet and very tangled, now it's back to normal silky-smoothness  *yay*

Almost a month on from colouring I can see no real difference in my hair condition compared to pre-bleach/dye.

Thanks again everyone for their advice and in particular their suggestion to WAIT!

Now:

Looks lovely 🙂

Do keep an eye on the condition though. Many of the box dyes have silicones in them which mask damage.