I'm just wondering how it's possible for any organism to make the change from asexual reproduction into bisexual reproduction if evolution is true?
It's just "sexual" reproduction, actually.
Here's one idea, based on penis-fencing snails - asexual organisms -> asexual organisms with a mechanism for gene transfer (the vast majority of today's unicellular life) -> asexual organisms that require gene transfer to reproduce (sexual now, but hermaphroditic) -> sexual hermaphrodites, now evolved to multicellularity, where the offspring gestates internally, incurring a biological cost of resources and vulnerability -> sexual hermaphrodites with a biological mechanism to determine which gets to gestate the offfspring -> sexual hermaphrodites where some individuals have phenotypical structures to aid internal gestation -> sexual, sexed organisms where one organism is fated, congenially, to bear offspring and the other to provide necessary genetic material.
It's sketchy, but based on organisms that exist to this day, and doesn't require going from genderless organisms to full-on sexual reproduction in one single mutation.
Now I would like to hear if my example is flawed in any way.
Well, the part where you make it up that an organism can only reproduce once is a little sketchy. Most organisms are capable of the production of many, many offspring over the course of their lives. An organism that could only reproduce one offspring once would not be able to build a population because it can only replace itself.
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