How can a haploid plant be bisexual?
Meiosis does not determine sexual form. Eukaryotes use meiosis and fertilization to recombine genes to form new combinations.  Meiosis does produce haploid cells from diploid cells, but that has nothing much to do with the sexual forms involved.  

In the case of the algal genus Chara, the organism's life cycle is entirely haploid except for the single-celled zygote formed during fertilization; this is called a haplontic life cycle.  Being haploid does not require an organism to be of one sex (or any sex), so there is no difficulty to being monoecious and having both male and female structures on a single organism.  The reason for having two kinds of gametes, sperm and ova, is simply practical: the specialized job of sperm is to move to another gamete, adn the job of the ova is to provide a maximum amount of nutrition for the future zygote (which means larger size and hence limited mobility).