I know HQPlayer well and its developer Jussi Laako, owner of Signalyst.
As you may know, HQPlayer has a powerful and extensive set of up-sampling filters, ditherers and modulators for up-sampling PCM to higher PCM sample rates, and converting and up-sampling PCM to DSD if desired.
This is the raison d'ĂȘtre of HQPlayer and I don't believe comparing it to BASS makes much sense. BASS is a library which developers across platforms can incorporate into their apps.
I'm still learning BASS, and I see it does have some sample rate conversion (SRC) capabilities; but this is not where it's emphasis lies.
It would make more sense to compare it with it's related player XMPlay which, I believe, uses the BASS library.
I believe XMPlay is very flexible and can support VST plug-ins. So up-sampling could be performed that way.
The up-sampling capabilities of HQPlayer are quite unique though and can't be equalled by any other player, in my experience.
I doubt if the kind of powerful up-sampling filters; etc. which HQPlayer incorporates are likely to come to BASS or XMPlay anytime soon, as I believe they are proprietary to HQPlayer.
HQPlayer is also cross platform, as is the BASS library; but XMPlayer is for Windows only.
I hope that helps answer your question.