Solved it. I installed Dell Bluetooth Application R205174. Strnage thing is that my laptop Studio 1555 is NOT in the list of compatible systems for this application. Yes, it works just fine! What's more, I think it was pre-installed on my new laptop as well!
The Dell EDocs available in Start Menu -> Help and Support mentions a Bluetooth Operations and Settings dialog that I'm supposed to get when I double click, or right click and select Control on the icon of connected Bluetooth devices. (This help article is also available from Broadcom here.) I'm not getting this any longer after uninstalling several Dell softwares from my new Studio 1555. (I used to get it before - a very feature-rich dialog-box allowing one-click access to features offered by the connected Bluetooth device like make a call from the mobile while using the laptop's mic and speakers, etc.) Even installed the latest Bluetooth drivers from Dell Support.  The Bluetooth application from Broadcom (downloadable here) fails installation with the error message "This program cannot upgrade your software. Please contact the manufacturer of your Bluetooth device for support." I have a Dell 370 Bluetooth card. Bluetooth itself works perfectly fine, though I'm not able to access several of the features offered by my device just because I don't have the application on my laptop. Please help. Thanks in advance.
Bluetooth menu in Vista Home Premium 64