Unfortunately, due to changes in the OS and how programs run, a program written for Windows 98 will not run under Windows 7 directly.
Even the compatibility mode will probably not work unless your version of Bicycle Pinochle for Windows was written for XP as well as Windows 98. (The WinXP version would possibly run under the Windows 7 32-bit version; it won't work under the 64-bit OS. To find your version of Windows 7, click Start > Control Panel > System and Security > System. If the version title ends with x64, you have the 64-bit OS. Otherwise, you have the 32-bit version.)
You need to either upgrade your game software or get an older version of Windows running somehow. This could be a virtual computer (runs inside your Windows 7 computer if your hardware permits it), a second machine or a dual boot computer. For Windows 98, you will need a licensed version of the OS for any method. Check a nearby Windows User's Group to see if anyone there has the OS.
If your version of Pinochle could run under Windows XP and you have Win7 Pro or Ultimate (or upgrade to them), you can run a virtual version of XP for free. In this case, download and install (in order) Virtual PC and XP mode from Microsoft. Then install the software in the XP computer as if it were the only computer running. (The compatibility mode didn't work inside XP mode for software written for Windows 2K so I doubt a Win98 program will work.)
An XP version of Bicycle Pinochle was offered by Microsoft: http://www.microsoft.com/games/bicycle/card/
. A Windows 7 version of Single Deck Pinochle is here: http://www.sac-irca.com/pino.html
I wish that I had better news for you.