Warning = Going off on a hair color tangent for a moment ...
I was going a darker blonde with Light blode on top. I used a Dark Blonde haircolor I bought from The Dollar Tree ( Yes I know Stupid for thinking "Hey I 'll get what I want for a buck!") So I colored the Bottom layer and it just didnt look right the cream was dark red! so I washed it out and this is what I had!
There is a Sally's, about 20 miles away
(*'mind you, I'm not an expert, but I used to be a hair dresser, and when I was working in that area, color was my specialty, before I left to focus on another job/my own clothing store, way back when.)
Sorry, it took me awhile to get back to computer ...
WOW! I think it looks good!
People pay big bucks to have their turn out like that!
But I understand that it might not have been what you were looking for.
1st thing to Consider = It WILL FADE gently with every wash 
You might just want to wait it out, and just re-dye it when it's longer or after your next haircut.
If that's the route you go = buy some dandruff shampoo (aka "a hair colorist's worst nightmare")
This Slowly FADES the Color with Every Wash ... PLUS ... Consider some blonding shampoos/conditioners, to gently tone down any left over red/brassiness, as it's slowly fading from the dandruff shampoo.
IF you decide it NEEDS TO BE FIXED & NOW = Things to consider =
Note : These are things that anyone will run into when they try to fix red, even a hairdresser. It's the nature of the chemicals really = one never knows exactly what the results will be, until AFTER they are tested & tried on the hair.
Some Hair Coloring Facts =
COVERING RED DYES, without going too dark, is tricky ... & the red could still shine through anyways.
REMOVING RED DYES, with some form of color stripper/remover, bleach or a lightening hair dye = most often times, the hair color results are rather orange-ish to bright orange. Not so much with more newer color strippers/removers ... more often with bleach & lightening dyes, especially without neutralizing additives.
In your case, I THINK that you like the upper color blonde (is that correct?), a
RINSE won't help much to calm to the red ... because the rinses are temporary/semi-permanent "fixes/adjustments" and are very liquidy = hence they will surely effect the pretty blonde you have on top.
Knowing that, My advice / suggestions :
NOTE = IF you really want to make sure that the top blonde is NOT effected = CAREFULLY, prep the hair by sectioning out all the pretty top blonde hair, that you don't want colored = get assistance, and possibly a 3-way mirror & a good light, so you can see it clearly. Also, consider CAREFULLY, applying vaseline on the base of the good blonde hair to prevent color seepage up into that area, even on it's roots ...
option 1. Try a permanent or semi-permanent COOL medium blonde dye on the bottom = that's a blonde with a "blue base", to help neutralize the red & copper tones from the red dye. ...
If it's not neutralized enough when you are done (meaning too brassy or red still), wait a day or so & try a toner to help neutralize it a bit more. OR get some BLONDE shampoo (it's purple) & / or conditioner, to gently neutralize it daily ...
option 2. Try a color remover/stripper on the red part underneath ...
This is a re-dye PREP step = meaning = this would help you get the hair back to a more neutral state so that you can redye it, to a more preferred hair color. ...
I prefer to only use WATER with these strippers, since some can be a bit harsh.
There's a good chance that it won't turn orange-ish & you'll be fine. But just in case it does = don't freak out.

The above toners & Blonding Shampoos/Conditioners will definately help.
HOW TO GET THIS DONE =
You COULD TRY to find a hair dresser to do this for you ... but please keep these things in mind =
a truely talented, experienced & enabled color specialist is hard to find! Not ever hairdresser is a color specialist. ...
(*ppl don't get mad at me for saying that = it's the schools = they cover the basics = vast amounts of color training & experience is usually only available as private studies in HUGE, name branded salons = positions are few & far between = that's just how it is in that business.)
Also, most normal hairdressers usually don't go out & buy things special (a few do/can, though), and they usually use what's in their shop = some are contracted to ONLY USE what the shop supplies in their back room (it's part of how the shop makes money on the supplies, from the hair dresser's services) ... so, they might be limited or restricted on what they have available to use, chemical-wise.

Most won't tell you this fact (or can't by contract), and most will/can not OFFER to go get the stuff that you may really need for this specific job. ... Plus, they are limited on / charge by TIME, in most cases = and color correction does take much time, and sometimes 2-3 visits a few days apart, to fix it right.
Going to a hair dresser may just be as much of a gamble as going to Sally's Beauty Supply, and doing it yourself with a friend or DH helping separate it. It will definately COST ALOT MORE! And there's no guarantee it'll be fixed correctly in one vist. ... like in my best friend's case = the last time she had to get a hairdresser to help her with her hair color (I wasn't available), it cost over $200-$250 per visit (times two) & she still walked out with orange stripes, that I had to fix later anyways.
I'm
not trying to scare you = Just FYI what people don't usually tell about this topic.
If I were in your shoes, I'd buy some dandruff shampoo, and some blonding shampoos/conditions, and wait a month of two = THEN try to fix it myself (maybe with a friend, if I want the hair separated again) ... but that's just me.
But really =
It looks great, the way it is ... Good Luck! Hope this helps.