- During travelling through bus, I don't like to take food.
- While travelling on bus, I don't like to take food.
Which one sounds good? And why another will be wrong?
I would say
When travelling by bus, I don't like to take food.
Travelling through bus.
means something like "going from one end of the bus to the other".
The word while does not work right to me, because I presume that you wanted to say "I don't like to take food (cooked home or bought) with me when I take bus rides". You cannot get food when you're already on the bus, which while implies.
To my AmE ears: When travelling by bus, I don't like to take food seems to mean, you do not like to carry food with you on a bus.
While travelling by bus, I don't like to have food would mean, you do not like to eat when on a bus
I do realise that take food can mean eat food, but is usually used by non-native AmE or BrE speakers as it's more of a literal translation from the original speaker's language
I would suggest that the best sentence to convey your meaning is:
I do not like to eat while traveling on a bus.
The first sentence starts with "During traveling". In English, two '-ing' words are rarely found together, and would normally be considered poor phrasing.
The verb 'take', particularly when associated with travel related words, normally means to carry or bring, rather than to consume. As your other comments make clear that you mean to eat, I recommend using that word.
As for the word food, when a person eats, food is clearly implied, so you would only include a modifier if you were eating something other than food.
Lastly, the phrase 'on bus' involves a dropped article. While this is increasingly common in British English, most American readers would find it odd; 'on the bus' or 'on a bus' would be the preferred choice in American English. I don't believe that British readers would find the inclusion of the article odd.