In Germany too, few commuters take the bike on the train. With integrated public transport, you usually get to within walking distance of your destination quite fast and reasonably comfortably. Some people then leave a basic bike at the station/underground/tram/bus stop to cover the last few hundred metres. Such "walking replacement devices" are often old/cheap ones that people happily leave over weekends or holidays as they are not likely to get stolen.
As Rosie said, tourism is a different matter. Germany has the advantage of having a very dense rail network with frequent services, which would be more difficult in large parts of Scotland. On the high-speed Intercity Express (ICE) trains, I've never seen a bicycle or noticed dedicated space. The slower Intercity (IC) trains have some limited bike space (needs to be reserved). But on the same lines there are regional trains. Regional Express (RE) trains stop only in larger cities and are often almost as fast as the IC trains, while proper regional trains stop everywhere. Both RE and R have several multi-purpose spaces, sometimes dedicated to bikes but more frequently just an open space the size of 1-3 compartments with foldable seats where people leave anything larger (bikes, ski, rucksacks, whatever), and if you want you can sit on one of the foldable seats and hold your bike. You don't need a reservation and I think the bike is free.
Regional express trains between larger cities are quite long and even whole school classes on a bike tour can find space. Regional trains into the more remote or smaller towns are often only 2-3 carriages but two families with bikes should find space.
The point is really that there are different kinds of trains serving the same destinations. In Scotland/UK, if I want to go to Aberdeen or York, I think there is only the Intercity, isn't there? In Germany, between let's say Nuremberg and Munich or between Frankfurt and Cologne there are ICEs where bikes difficult or not possible but also REs with plenty of space.
Regional day tickets allow you to use any regional train in a certain area. For example, the Bavaria ticket costs 23 Euro for one adult (plus an unlimited number of own children) or 28 for 2 adults (plus unlimited number of own children) up to 43 Euro for 5 adults (plus children). It's valid all day on weekends and from 9am on weekdays until 3am next day.
These tickets are quite popular with families and also groups on a day trip to the country. Or you can try to cram as many train journeys as you can into a day...