Any strategies on how to get started with collecting customer reviews on a new comparison website?

Can you clarify the question more? Do you mean how do you scrape an existing website for reviews?

I'm building a website where people can find bike sharing services near them. User reviews for all brands are a way to get started in my opinion. My question is how can I manage to get users to write those reviews on my platform.

If reviews are all you're after, one way might be to leverage your existing network - friends / acquaintances that you know use bike sharing schemes. You could either ask them directly to review the schemes they've used on your site - or if you'd rather remove the step of them signing up, you could just ask for their opinion of the various schemes they've used; then once they've given their opinion ask if they'd be happy for you to quote them as a review on your new product.

Thanks, this is what I already did. They don't have to signup. They can review directly on the brand page e.g. But that's only a few people, so doesn't get it really started.

Being brutally honest, you can't force user behaviour. Seeding data with people you know is always a good start - but did you also get honest feedback from the people who seeded your data? Are you solving a problem for them? (Since clearly they use schemes).
I personally use bike schemes, but for me the existence of reviews isn't going to be a driver for me to this site. My own initial feedback on this is that you're missing a map view and a list view.

Thanks for your feedback, will definitely try to add this. I think if you are in a city (e.g. Berlin…) and you can choose out of 8 schemes... some opinions on each scheme will add value. Anyway, do you mind giving your opinion about the schemes you used on the website? 😃

I used MoBike in Berlin because I already had the app installed from using it in London and already had credit on that app and a bike was already right there in front of me.