As far as cycling is concerned the only visa that you can really use is a Transit visa and you are likely to be just cycling 550km across the country to get from one border to the other.
The transit visa is the only one that allows independent travel across the country.
You will only be given 5, 7 or 10 days.
You are only likely to get 10 days if you apply from your own country, although you can try begging.
You can get the transit visa just about anywhere there is an embassy.
There are Turkmenistan embassies in India, Kazakhstan, Uzbekistan, Tajikistan and Iran.It takes between 10 and 14 days if you don’t have a LOI.
You have to complete two forms which are slightly different, provide two copies of your passport and two passport photos (women with hair covered is advised)
You don’t need to leave your passport at the embassy so you could go and pick up other visas while your application is going through.
When you pick up your visa you must have a valid visa for the country that you are transiting to: ie. Iran or Uzbekistan.
You may get your visa more quickly if you already have your transit country visa when you apply. This is what people who regularly transit the country do.
Letter of Invitation (LOI)
This isn’t necessary but you might get your Turkmen transit visa a little more quickly. You can get an LOI by hunting around online. The costs vary.