bump into sb vs bump with sb

Hi there!

I would like to introduce myself the first place. I am new to this forum and I am looking forward to making new acquaintaces here.
I am a 18 year old student from the Wrocław area and I am planning to take the CPE Exam right after my Matura Exam, this year.

Now, let's pass on to the crux of my question:
I've been trying to conjure up such a sentence:

"The world is so small, pal. As you see, we cannot simply move abroad without bumping into each other"

This sentence looks fine to me, BUT I'd taken into consideration another possible option:

"The world is (...) without bumping WITH each other"

This also seems quite correct for me, but I am not sure whether or not it is appropriate.
Your thoughts?

If it means anything (maybe fighting?), it's not equivalent to 'bumping into'.

BTW, it's 'an 18-year-old student', and you probably meant 'go abroad', not 'move abroad'

"move abroad"is exactly what I meant.
The context is that one of these guys moved to a different country - to work there - and then, he met his friend on the street.

Into

Not so long ago (well, maybe about 30 years ago) there was a dance called the Bump. Then you could 'bump into somebody. Worth researching on Uncle.

I want be a good speaker and amazing writer. I want everyone impressed with me. But, when I’m writing …. blank, lost ideas. When I’m writing a story, I want it turn out as a nice story that makes anyone who reads my story impressed. I don’t want to make a clichéd one . But, as noted, I’m lacking ideas. My teacher tells me that you need to read, to enrich your idea, vocab, grammar and so on. I admit that I’m not a bookworm .

I want TO be (nighdy nie slyszalas ...to be or not to be?) a good speaker and (brak przedimka) amazing writer. I want everyone (brakuje 2 slowa) impressed with me.
..But, when I’m writing …. blank, lost ideas. ...wg mnie to nie jest calym zdaniem..
When I’m writing a story, I want it TO turn out as a nice story that makes anyone who reads my story impressed.
My teacher tells me that you need to read, to enrich your 'idea' (chyba masz zamiar miec wiecej jak jedna), 'vocab' (prosze pisac slowa w calosci...to nie jest calosc tego wyrazu), grammar and 'so on' (Teacher tells you to ..so on? - co to znaczy? Nie rozumiem)