I cant help with the crocheting of triangles (sounds very complicated) but over the years i made heaps of BD scarves and all were done the same way (like the bought ones)
Thread the beads onto your crochet thread - you are going to need a ton of these so using a beadspinner helps(http://kimberlychapman.com/crafts/beadspinner.html
Crochet a long enough chain to comfortably fit the bottom of the scarf. (I sometimes used to then crochet a line of sc just to make handling the beading easier but it is not neccesary.)
Crochet 5 chain stitches adding a bead into each st. Sc into the 3rd ch of the previous row. Ch 5 sliding a bead onto each chst, sc into the 3rd chain. Contonue making these little "loops" untilthe end of the row. Turn. You will now have a row of unbeaded chains topped by loops of beaded chains.
Ch5 slipping a bead into each chain, sc into top of loop formed on the previous row. Ch5 adding beads, sc into top of next loop.
the process continues until your edging is a wide as you want it. On the last row you can create little tassels by making a stitch with several beads instead of 1 and then sc into the ch at the base and make another 2 or 3 loops with many beads each time anchoring them into the last chain stitch.
You can also crochet the edging "sideways" where you do not make a long chain first but crochet directly into the fabric and your little diamond shaped loops are made sticking out from the fabric with the tassel being on the turn. Mmmm... don't think I explained that very well... sorry!
If you want to know more please feel free to ask me to re-explain
I usually preferred making the long chain and stitching it onto the fabric as it is very secure and when your fabric wears you can unpick the beads and use the edge again. Saves hours of threading beads on!
I dont know how much beading you have done so please forgive me if I am repeating stuff you know, but beads are made of glass and some have extremely sharp edges - the main cause of the bought scarves fringe unravelling is from a sharp bead edge cutting the thread. You can prevent this to a certain degree by really checking your beads well for sharp edges .
Also keep in mind that the cheaper beads (which we so love to buy by the kilo
) often have varying hole sizes and many beads have very
small holes so take the thread you intend using and try it out with a sample of the beads before you buy a ton. The bead hole sizes can vary in a batch by quite a lot so check a few beads, not just one!
I know the bought scarves have crochet thread they use but for my practise scarves I used a type of fishing line called spiderwire or fireline. It is a pain to crochet with but has never ever broken on me - even when caught on someone elses cane!! Yup those cane dances can get wild
This site has some good tips on bead crochet and knitting: http://www.swallowhillcreations.com/FAQ.htm
As has this one: http://www.beginnercrocheting.com/How-To-Do-Beaded-Crochet.php
and here: http://www.beadingdaily.com/glossary/crochet.aspx
There are also some good demonstrations of general beaded crochet on utube, which may give you some more ideas.
Happy beading/crocheting and dancing!!