Cycling in Berlin can be a pleasure, most car drivers are cautious when it comes to cyclists, though there does exist some antipathy between the two groups. When you come to Berlin, skip the bike tour. Rent a bike instead!
I have a secret to confess. I hate those awful bike tour groups. At first when they began to appear, I was enthusiastic and sent all my out of town guests to sign up. Now that they are everywhere, I have to say skip it. You see them all over the city, like some distended, orange safety-vest wearing snake, clogging intersections, blocking traffic, generally making themselves a nuisance, while the tour guide, who probably only moved to Berlin last week, embarrasses himself trying to speak loud enough for the whole group to hear.
So, while I take no responsibility for your safety, all you need to do is find a bike. You already have the best guide to the city right here. These days you can rent bikes practically everywhere. Lots of cafes even have bikes to rent at a reasonable price (from € 10/day). If your bank card is equipped with a chip, sign up to use the amazing Callabike from DeutscheBahn.
Just remember: don’t ride on the sidewalk, traffic coming from the right has right of way, police may stop you if your bike hasn’t got lights and a bell, and you can take your bike on public transport but you’ll need to purchase a ticket for it.