This is the simple difference: By bus = a means of transport On the bus = a location In this context, you can use either : 'I came home by bus' and 'I came home on the bus' both give us the same information. They're not always interchangeable, however: 'By bus' always combines with a verb of movement, such as 'come', 'go', 'travel' or 'arrive': it tells us HOW the person travels. For example, '90% of commuters in this town travel by bus' or 'It's easy to get to London by bus'. This is the only way that 'by bus' can be used. 'On the bus' doesn't necessarily describe a mode of transport: it can simply tell us WHERE the person is at a particular time. For example, you might phone or text someone and say 'I'm on the bus. I'll be home in 10 minutes!'. Or you might say 'I'll meet you on the bus.' or 'I always listen to podcasts when I'm sitting on the bus'. These are all examples of phrases where only 'on the bus' is possible. NB Nobody says 'via bus'.

Further to these excellent answers, just be aware that 'by' in different contexts can mean 'near' or 'next to'. Eg. I saw him standing by the bus. As long as you avoid that mistake you should be fine.

They mean the same thing here. But they have slightly different meanings in different contexts. Literally, "by bus" means "by using a bus". But "came home on the bus" could potentially mean I "came home, to my home on the bus" (thus my home is on the bus) - this is of course a very unlikely interpretation, so few people would misunderstand these words, but just for better clarity it's better to use "by bus" or "via bus". "Via bus" is even better than "by bus" in very formal language, because "by bus" could potentially mean "beside a place, thing or person called Bus" (especially if spoken, because in speech the lack of capitalisation can not be seen). However, "by bus" is usually more appropriate for casual language in order to avoid sounding pretentious and creating hostility within a social setting, because the word "via" is a bit posh.

No difference. You can use either one.

Used in this way - no difference. Not universally interchangable though. . I met him on the bus. I met him while traveling by bus. On the same bus as you? difficult to use "by" here.