See my updated working solution(UPDATE 2) below to configure tilting in Bluestacks app.
As the tilt function is working fine in other games. It is dependent on the games that you play and its support on the Bluestack app player. Once the game is supported it will show a popup of the controls that can be used to control the actions and mimic the accelerations. So for example when playing a game like Labrynth Lite, after installing and opening the game the app player resized the windows like a phone and showed the controls using the arrow keys.
Screenshot - click to enlarge image
As this shows that the keyboard controls are app dependent and Bike Race doesn't support the tilt controls in Bluestacks(v.0.9.25.5401) as of now.
Update 2 - Working Solution:(06/Jun/2015 01.43 IST)
I actually found out how to mimic the tilt functionality in all games. The first thing you have to do is to configure the tilt motion using the key mapping functionality provided by the Bluestacks app player. Here's what you want to do,
Open Bluestacks, and click the keyboard icon shown first in the bottom menu (along with share, fullscreen and exit icons aside). This opens the configuration window to configure the Dpad, Tilt and other such Kep mapping functionalities such that you can control the object using those keys and mimic the tilt in the games.
After Clicking the Tilt option in the menu shown for key mapping, Click each Rounded buttons and press any key in the keyboard to configure that key as the key to make the control for tilting. Likewise set the controls for tilting Left, Right, Up and Down. Set the sensitivity to default and play the game once and set it according to your needs.
Once you click confirm and it will show you the Keys that you have configured for each tilt functionality. You can see the configured keys for tilting is displayed as I set. Eg. For tilting the bike backward I need to tilt left so I set the Left tilting to Left Arrow key mapping. Set the Key whichever is convinient for you and you should be able to do the tilting in all games you install on Bluestacks.
More in the support site
Happy Gaming!!! ;)