Check your accessory and run relays and see if it is stuck closed. Good way to find a parasitic draw is to grab a cheap 30$ tiny amp clamp (one that is only an amp clamp with no other features, as cheap amp clamps have no internal interference filtering) and clamp over every wire with the bike 100% off until you see amp draw.

Otherwise, check output voltage of your stator while running the bike by observing the voltage at your battery. You should see 13.5-14v when the bike is running then a drop off to 12ish volts when you shut the bike off. Your battery needs a voltage differential to charge properly, and if the voltage is too low, your stator is likely bad.

 

Get the battery charged , then start the bike see if you get 13.8v at the battery. If you don't have it you need to fix the charging system. The 1100 is known to have trouble with the voltage regulator before needing at stator.

 

V-Star 1100 Wiki Knowledge Base - 1 New Owner "MUST READ" Section look under repair to check the charging system. when you open the site the top right corner has the sections. VS-1100-chagre-syst.pdf

 

Battery keeps draining

I have that problem also but it has nothing to do with any of my vehicles.........

 

So ya got a brand new battery that we can assume to not be faulty in any way. And as a replacement. We can assume a typical maintenance-free of 12ah capacity.
But after a days trip,... it's dead.

Because the headlight alone draws about 4½-5amps, the light alone would deplete the battery below usability in jus 3hrs time,... less with additional loads of other running lights and occasional loads of starting engine.

So you could likely assume that the battery is not being charged with engine running.

Some quick simple checks will verify that issue.
First- you'll need to remove or fully disconnect battery from the bike, and FULLY charge your battery again.
Pretty difficult to determine that a sealed maintenance-free is fully charged as the electrolytes specific gravity can not be easily measured to assure full charge capacity.
So easiest is probably a charging with known charge rate for the time necessary to fully replenish battery. Assuming a constant 3amp charge rate, it'll take about 4hrs to fully charge. Since most chargers today are 'Smart Chargers' with variable charge rates,... best to charge for a prolonged period of time to assure full charge.
A fully charged battery at rest, SHOULD read about 12.5v with a multimeter.

Next-reinstall/reconnect battery into bike. Assure tight clean connections.
Again, measure standing voltage after installation,... SHOULD still be 12.5v
IF,... jus a tiny drop of voltage IS noted when connected, then a parasitic draw of a defective componant is likely OR a leaky wire of poor insulation, corrosion, ect., is present with neeed repairs requiring attention.

NOW, turn key on, start bike and again check battery voltage. With bike running at sufficient idle, voltage should be reading about 13.5v,... and at higher engine speed, about 14-14.5v.
If these higher voltages are NOT present when running,... the charge system is likely defective, OR lacks connections to the battery.

Quite likely, the voltage regulator has failed. Further testing of charge circuit, regulater AND stator should follow to KNOW what exactly has failed, and it always helps to know WHY it failed.
No sense in replacing parts if the 'WHY' isn't identified & corrected.