You could pay 10 EUR a month to the Leipzig based company Nextbike for using their rental fleet within the city as often as you like (30 minutes of biking included in every lending process, afterwards extra fees apply).
(No affiliation)
If you are interested in taking longer trips outside the city, buying a used bike and selling it later is your best option.
In 2008, I shipped a bicycle from Germany to Sweden. I don’t remember the exact price but at the time it cost me less than €50. I did this primarily because I was moving to a small Swedish town in winter and was unsure if I would be able to buy a bicycle locally.
If you fly to Germany (which seems very likely), you can bring your bicycle on the plane (boxed). Shop around, you should be able to find an airline where it costs (much) less than €100. If your bike is indeed good, it should be worth it, for a secondhand €100 bike will be an OK bike but not a good bike. I did this when moving from Sweden to Canada and from Canada to the UK.
A final option, which for most people is in fact not an option at all, would be to find a ferry across the Mediterranean and ride your bicycle, but this would be a highly adventurous option, in particular since you would apparently need to cross Libya to reach any operational ferries in the first place, so this is currently not to be recommended.
Another recent option is a Swapfiets. You pay a monthly fee of currently 17.50 Euros (15 for students) and get a decent bike, repairs included. Contract duration is one month. They’re not sport bikes, but should be sufficient for inner-city transportation and occasional longer trips.
(No affiliation, I just think this is one of the cases where their offer actually makes sense. For permanent residence, getting your own bike is cheaper, and for shorter trips you’re better off with short-term rentals like nextbike).
As already said, the best option would be to buy a used bike. You can find very good offers on eBay kleinanzeigen. You can find a good bike even for under 50 EUR.
Another option is wo-bleibt-mein-fahrrad.de. They buy, sell and repair old bikes in Leipzig. I’m not sure if that would be useful for you, but maybe there are some interesting cheap bikes.
Credit:stackoverflow.com‘