Oh gosh, I remember those days. It really does get easier (twins are now 10 months).
There's 20 months between DD1 and the twins so not sure if my "routine" would work for your 3 year old.
My bedtime routine started around 4pm when I would breastfeed the twins. Mid feed, around 4:30, I would get DD1's dinner. She would eat it IN FRONT OF THE TV (what a bad mother I am) whilst I finished feeding the twins. The babies would then have a quick nap from 5 and I'd wake them at 5:30 to give them a bath.
I would get DD1s milk, towels, grobags and all the bed stuff ready before plonking them all in the bath together (I had two of those generic plastic moulded seats for the babies). I would then prepare myself for three screaming children and get whoever was crying loudest out first, dry them and dress them. Repeat for the next two. By this point I would be losing the will to live. I would take us all into my bedroom (it's now 6pm-ish) and stick the TV on again and give DD1 an array of books to look at. I'd feed the babies whilst trying to avoid being bitten by DD1 (who was going through a biting stage).
If the babies fed well, I would put them down in their cot (sharing at that stage) and take DD1 to bed and read her a story. If they hadn't fed well, I'd prop them up on my bed and read DD1 and excelerated story then get her off to bed quickly so I could continue feeding the babies. DD1 would always be in bed by 7 (for my sanity).
As I write this it's all come flooding back so you have my sympathy. You'll work out what works for you, please try not to be too hard on yourself. They don't need to be bathed every night, they don't all need to be bathed together - you could bath the babies in the morning/after your other child is in bed. I found my DD1 was most accommodating when I got her involved - washing their hair etc.
It really does get easier - bathtimes are a joy now. Be kind to yourself and give yourself a pat on the back for even attempting bath/bedtime in your own.