Yes, there is a amp draw by the inverter itself, but it isn't enough to explain your problem. The inverter overhead should be in the 0.3-0.8 amps/hour range for that size inverter.

A 60w light bulb requires 0.5 amps/hour @ 120V. To get 0.5 amps @120V requires 5.0 amps @ 12V (5 amps x 12V = 60 watts), so your little bulb id actually drawing 5 amps plus the inverter overhead from the battery. And your 100 amp-hour battery can actually produce only about 50-60 anp-hours before the voltage falls below the minimum needed for the inverter to function (typically around 10.0-10.5 VDC). That assumes a new and fully charged battery. An older battery may be only 50-75% of that.

How long did you charge the battery? It usually takes

__at least__ 24 hours with a typical 10A automotive style charger to get a battery to full (100%) charge. The charger puts out 10A only when the battery is very low on charge. The rate quickly tapers off to 5A and soon only 1-2 amps/hour, so getting the battery above 80% charge takes a long time.

How did you determine the battery was down to 10% charge? Most standard battery test tables or meters base a percentage like that on a voltage of somewhere around 11.5V or a specific gravity of about 1.07. That level will typically be reached after about 40-50 amp-hours of power usage. The 100 a=h rating assumes the battery is run completely down. Here's the definition of battery amp-hour rating, courtesy of Optima batteries:

The Amp Hour rating tells you how much amperage is available when discharged evenly over a 20 hour period. The amp hour rating is cumulative, so in order to know how many constant amps the battery will output for 20 hours, you have to divide the amp hour rating by 20. Example: If a battery has an amp hour rating of 75, dividing by 20 = 3.75. Such a battery can carry a 3.75 amp load for 20 hours before dropping to 10.5 volts. (10.5 volts is the fully discharged level, at which point the battery needs to be recharged.) A battery with an amp hour rating of 55 will carry a 2.75 amp load for 20 hours before dropping to 10.5 volts.

I suggest that you charge the battery for 24-36 hours and then test again. You should be able to get 8-10 hours before the inverter shuts off or gives its low voltage alarm (does it have one?).