The area around Bratislava and western Slovakia is generally safe. Don't expect any raiding bands of robbers and thiefs in the woods or gangs in cities at night (*). Pickpockets are most common in public transport vehicles in larger cities.
When wild camping, make sure you lock your bike and take any valuables with you in tent. As the saying goes "opportunity makes a thief" so if you follow common sense, you should be allright.
People aren't bad, but if they smell that you have a lot of money, some of them will try to make you share some of it. Maybe accidentally miscalculate price in resturant or in a taxi...
However the biggest risk are the car drivers. If you're coming from the western part of Europe (France, Austria, Germany, even Czech republic) you will notice how careless the drivers are. They won't give you much space when passing, and will pass in dangerous situations. There are areas where motorway isn't finished yet (or simply isn't available at all) and all traffic must take primary road. It is best to avoid such busy roads whenever possible.
The quality of road surface is often miserable. Potholes, pothole patches, manhole covers. Moreover only some roads have shoulder wider than 50cm. The majority of roads only have something like 20cm shoulder and cyclists must use the car lane.
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* there are some ethnic communities in the central and eastern part of Slovakia, living in very poor conditions and they have quite different sense of what's good and bad. I would avoid those areas. There were rumors of some children attacking cyclists with stones...
