You have a few options.
Most strait forward (as suggested by @Jeffrey) is you can just type plain text in Bike (including markdown formatting). Benefit is you can type and organize in Bike and copy/paste into a Markdown editor. Drawback is you can’t use Bike’s built in formatting commands.
Second option is to use an external tool to convert Bike’s rich text from the pasteboard into Markdown when you are ready to export. For example you could try:
https://euangoddard.github.io/clipboard2markdown/
Then go to your rich text Bike outline, copy the text you want converted into Markdown. And past into the above linked site. It’s not perfect. For example it will not convert Bike row level formatting (headings, ordered lists), but it does work pretty well on the inline formatting: bold, italic, links…
A third option is to make a dedicated converter from Bike to Markdown. There are many different ways someone might want to turn an outline structure into a Markdown document, so there isn’t really a best solution out there. There have been a number of scripts shared in these forms though that perform this process.
Here’s one to look at:
Here are some older scripts: