How dow you say "NIGAWARAI" in English?

As  you know writing this diary in English is the best way to improve my English skill constantly.
So I always thank to people who suggest mistakes, better expressions, etc.

Yesterday I used the phrase "a bitter smile".
And my friend advised me that an ironical smile  be better.

I thought again.
What I want to use a word in Japanese is "NIGAWARAI".  "NIGA" means bitter.
So I used the word "bitter smile" simply..
"NIGAWRAI" has broad meaning. However "bitter smile" doesn't seem to have as broad meaning as "NIGAWARAI".

I learnt bitter smile includes resentful feeling.
It is OK to use NIGAWARAI including resentful feeling in some cases.
However, when I used the word of bitter smile in the diary, I was not resentful.
So using "a bitter smile" was incorrect.

However I wouldn't include any ironies, even it sounded ironic.
So the smile I showed at that time was not an ironical smile.

Probably I had a wry smile. How about it?
According to my dictionary, the word of wry includes not only ironical, but also puzzled.

Or just it might be enough saying "I grinned".