I think you have to install Bridge.
And really, without telling us what you do, it’s not possible to tell you what to install.
... in order to have InDesign 5.5 run properly.
For that you only need to install InDesign.
I opted for InDesign, Illy & Bridge - skipped Photoshop and Acrobat and et al.
I do mainly print and I'm perfectly happy with CS5. The current upgrade deal allows me to have 5.5 and 6 for a one-time cost, and it gives me 5.5 in case a client sends me an InDesign 5.5 file. I'm not even planning to use it unless I have to. I can wait for CS6, which is supposed to appear in less than three months.
All I want is to be able to work in 5.5. if I suddenly have to. Otherwise I'll move from 5 to 6. I will try Jongware's advice even though I have a murky remembrance of advice saying to install Bridge (that's why I asked). From CS 1 on up, I have always installed the entire suite, but since there's so much duplication in 5.5 I only want InDesign (and Acrobat X). Daniel has probably provided a fall-back solution. Thinking about it, as I'm usually on deadline and don't need any software problems, I may go with Daniel.
If you want to use Mini-Bridge you'll need to install Bridge CS5.5, and you'll also need it to synch color settings across the CS5.5 apps.
Your question is confusing -- why would you ever not install everything? Disk space is cheap.
That said, If you have CS5 installed, it will save you annoyance to not install Photoshop and Illustrator from CS5.5, because they do not have CS5.5 versions. They have "CS5.1" versions that are essentially identical to the CS5.0 versions. But you'll have to worry about migrating your preferences over and it's just kind of annoying. So it's safe to skip them if you have them already installed.
And CS5.5 has Acrobat X instead of Acrobat 9. That is...a mixed blessing. Most people dislike the UI, but it has a few bugfixes (security and otherwise) and a few features added as well. I don't think Bridge changed at all for CS5.5.