Is there any significant difference between the sound of a horn with a detached bell and that of a fixed bell? It is something that I have been curious about since I started looking at buying my own horn.

No significant sound difference, although some players have optional heavier bells that they use ...

Some people claim that the extra metal in the detachable bell gives a bigger sound, but that's so far unproven. If I had it to do over again, I'd buy a detachable bell horn. Most of the pros have them. The carrying case for a horn with a detachable bell is compact & flat like a suit case & can slide under a bed or fit just about anywhere. But, as you probably know the carrying case for an attached bell horn is as awkward as a cow. Valerie in Tacoma

I have a Holton 200 with a detachable bell. I like the horn but not its detachable bell. Its tricky to put the bell on quickly and it encourages leaving the horn out of its case all the time. I prefer my Hans Hoyer double fixed bell horn. The shape and size of the horn case isnt an issue to me - but I double on BBb Bass and Sousaphone and those cases are large and troublesome!