Hiya!
Ok, I guess I'll say it yet again...

...
You're thinking "backwards".
I've said this multiple times since 5e has come out as a free PDF. There are a lot of people who are "new" to 5e's style of play (re: 0e/1e/BECMI style). These people, like the OP, go looking for rules in order to facilitate an idea. Close, but "backwards" in thinking. Bare with me...
What the OP needs to do is think of the set up, the situation, and then imagine how it would play out in a story or movie. Don't think of rules or potential rules at this point. Ignore all that for now. Just imagine it all...
I picture a road in the woods. The PC's are walking down it, casually chatting to themselves. Then they see some potential brigands up ahead...or maybe they are "but poor travelling circus performers"

The PC's go into suspicious mode (re: passive Perception v. Stealth of the bandits in hiding). They approach, and the folks up ahead put their hands on their weapons and demand tribute to pass "their road"...and that it would be bad for the PC's to refuse. The PC's stop and place their hands on their weapons. "So, that's how it's going to be then. So be it!" The bad guys draw weapons, the PC's draw weapons...then, suddenly, arrows fly from the sides! The PC's yell "AMBUSH!" and charge towards the original bandits.
Ok. Now that that scenario has played out in your mind...
now you go looking for rules to support that narrative. If you don't find them, you MAKE IT UP! Seeing as the OP has decided that "Surprise" seems like the best rule is understandable, as I believe he said he comes from a "3e" mindset...and everyone knows there are a billion ways of giving bonuses, penalties, adjustments and whatnot for AC, attacks, or any other numerous numbers to be crunched. But 5e isn't like that. It's fast and loose. It has a "Surprise" rule, sure, but as I said...think of the situation FIRST and then find a rule. If you can't find one to fit...MAKE IT UP!
So, I'd simply just say "Arrows fly from the bushes! [rolls some dice, some hit, some miss, some damage is dealt]. Ok, now it's Round 1. What does everyone want to do? The bandits in front look to move towards you to engage. You can all make out two bowmen on the left of you and two on the right, each pair about 30' away. They seem to be reaching to notch arrows to fire again". That's it. Simple. Fast. Loose. Don't try and "figure out" how the rules for Surprise would or wouldn't work in this scenario, because 5e rules tend to be of a "simplistic approach". In this case, Surprise obviously assumes "Side A and Side B". Not "Side A, Side B, Side B2, Side B3". If it helps, think of the PC's
and the bandits on the road as being Side A, and the hidden bandits as Side B. Side B has "surprise" (meaning the visible bandits and the PC's don't do anything the "surprise round"). Er, yeah, basically what I said the first time.
PS: What Chris Perkins was doing was the fallback...in other words MAKE IT UP! He just made it up, using Surprise as a base to MAKE IT UP. That is how the 5e rules are supposed to be used. Fast and loose, baby...fast and loose!
^_^
Paul L. Ming