I just did a booga bag too. It doesn't really matter what the pre-felted item looks like (ie. I wouldn't go and do a fancy bind-off) because once it's felted it all looks LOVELY!! Felting covers a multitude of mistakes and imperfections
. As far as it looking flimsy, that gets solved when you fold in the top sides and add the i-cord. I'd be more worried about the bottom being flimsy but you already did a double strand there so that should do the trick.