How is bonus experience used and counted?

Bonus experience is used when you perform that skill. In the case of Prayer, burying bones, spreading ashes, etc (I will note that the Ectofuntus in Port Phasmatys does not use bonus experience for Prayer, but guilded altars in Player Owned Houses do count). It sounds like you received either a prayer fallen star, or prismatic one, which allows you to choose a skill to use it on. These stars are earned typically from Treasure Hunter, or special events.

The way bonus experience works is when you perform a skill that has bonus experience, you will receive double experience for that activity. In the case of burying normal bones for prayer, you will receive 9 experience instead of 4.5 (the .5 is hidden when the experience is granted to you). This will continue to happen until you deplete the rest of your bonus experience (green number).

Note that if you want an item that grants experience rather than bonus experience, you'll want a prismatic lamp which comes in different sizes just like the stars. There are some other items that also grant experience immediately that you can get from Treasure Hunter, but are only found during special time frames. To name a few:

• Lava Lanterns
• Hydra Lamps
• Smouldering Lamps

Some of these items grant you both regular experience and bonus experience, or grant you regular experience while also consuming some of your bonus experience (if the selected skill has any) for a larger experience gain!