Check the label on the bulb, many LED bulbs are rated 90-240V.

If it's not rated for 120V, do not use it. Although the amperage is nearly the same / quite low, some components may fail and cause a fire or electrical fault.

What is the manufacturer and exact model of the bulb?

Nearly all electronics come with product labels by ETL, cULus, CE, CSA, FCC, etc. which contain their specifications (volts, amps, watts, frequency, country of manufacture, certifications).

In Canada, it is illegal to sell electronics without safety certifications. Installation of use of devices without proper certification may render your home or renters insurance policy invalid.

If your bulb not certified, then I would send it straight to electronics disposal. Otherwise, be very careful especially when using it for something it may not be designed for.

Here is a sample bulb label in my home (not used as a grow light):

It is rated for what you are using it for (120V) but has no safety certifications.

If it does draw more current for more than a couple of seconds, the fuse will blow, in which case, you should replace it with a higher ampere fuse.

But, correction, my bad, the current will almost certainly be more than 0.1A therefore you will need a higher amperage fuse. You need to measure the actual current used by your lamp and choose a fuse that is slightly higher. This is because, unlike DC, AC power consumption cannot generally be calculated from voltage and current alone. In a moment of senility, I forgot that.

One of the best investments that you can make is to buy a KillOWatt Meter for about $20. The meter has the ability to read amperage. After measuring the actual current consumption of your lamp, you will know what ampere fuse to use.

http://www.homedepot.com/p/Kill-A-Watt-Electricity-Monitor-P4400/202196386

LED lamps tend to draw the most power when cold and the least power after they heat up, so note the initial power consumption and current when first turned on.