What i was taught was for PLASTIC/RUBBER bumpers, was to get the bumper repair epoxy made for rubber bumper repair at an actual auto body paint supply place, not autozone. The stuff that body shops use (currently / vs fiberglass and fiberglass resin like they used to). you (in my opinion) don't want to use fiberglass on a plastic / rubber bumper because the fiberglass with resin is way way harder than a rubber bumper, and will crack if (and when) there is another impact, or.. when some chick inevitably sits on the bumper and causes it to flex or something, and you hear a little "crack" and feel your blood pressure go WAY up suddenly.
(i mention that because i just scalded my girlfriend for sitting on my bumper literally 15 minutes ago.... haha (this may be all for nothing if the bumper is in fact fiberglass, then of course you WOULD want to use fiberglass, as that would be blatantly obvious)
the stuff i'm talking about is a 2 part epoxy, you put it in a calking gun, and it turns into a dark grey color very similar to JB weld, but is meant to be durable, bendy and flexy like the original rubber, but strong, and bonds the pieces very well. and it, itself is NOT like jb weld...
Then, you go to Home Depot, and get some of that mesh stuff like they use fixing holes in drywall, or on seams, which is $4 instead of $25 and do exactly what coco said... it's right on the money, i just have a difference of opinion on supplies used.
BOEN 2 in. x 150 ft. Self Adhesive Fiflex Mesh Joint tape-FM-2150 at The Home Depot
don't get me wrong though, Coco's thing WILL absolutely work, and i mean no disrespect at all, it's just that there is better stuff out there that not everyone knows about. (not saying the mesh i'm advising is better, but it saves money over woven fiberglass, and the epoxy i'm talking about will go through it better than fiberglass (and this mesh IS fiberglass) not to mention sanding and working with actual fiberglass really really sucks..)
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Then from there, you probably want to have it re-painted, and, honestly, i'd just let the body shop fill in the front side of it rather than creating more work for them (*which means more labor hours, which means a higher bill, un-doing, fixing, and re-doing what you did) unless you're good with body work (most people aren't) ..
The BIGGEST problem with people and body work is, they do
unconsciously stupid stuff like;
fill in the V with the epoxy, and start sanding it smooth, but don't realize that their sanding block is CUTTING material from what is already flat while they are cutting the mountain of goop they created by filling the crack, or, they use their fingers and cut laterally, and end up sanding finger grooves into the base material in all sorts of weird directions and there are flat and high and low spots everywhere, thereby making a grotesquely uneven surface which will show up when painted as a wavy and warped piece of crap, when in reality, it isn't... well.......... wasn't.....
there's definitely a method and an art to body work. anyone can do it, but not everyone can do it well.
WITH THAT SAID: if you don't fill in both sides of the repair, it will not be structurally sound, and has a much higher risk of cracking and falling off again, so, if you aren't going to fix the visible side of it yourself, get it done and painted soon so it doesn't break off again.
(wish i remembered the name of the stuff i use, this whole post is kind of for nothing without it... i'll try to figure it out. )
I've repaired lots of bumpers with this stuff. the epoxy, like i said, is much more flexible than fiberglass resin. they always hold up, barring someone kicking it fairly hard with their foot, or hitting something like an 18 wheeler tire tread at highway speed, in which case, there's not much that will help. even carbon fiber would break in that instance.
you could always use a plastic welder to fill in the V but..... at your own risk. too much can go wrong, and you need to similarly match materials, much like welding metal. you use steel wire for steel, not aluminum for steel. you know?
not arguing with anyone though, just offering a different opinion and perspective
edit:::::
yeah............ just pay the 350 if they'll paint all that stuff too, just be sure you're going to a quality body shop or you'll regret it... check out some of the work they've done in person before you agree to it. if you don't see anything obviously wrong with their work as a layman, no one will notice the mistakes they make on yours.. hahahaha