A conversion to LED is the way.
You can get LED 'bulbs' that replace the old filament H4 bulbs but unfortunately the reflector type lamps we have arent really suitable.
Best and cleanest route is to get a whole LED lamp unit that replaces everything inside the chromed bucket on the bike.
A lot of people use chinese units off the Internet, then there's the legit but expensive JW Speaker units including ones with adaptive capabilities.
And there's also the (also expensive) Triumph OEM units (actually made for them by JW Speaker) which happily fit the old Rocket III too;
Was wondering if the Rocket 3 TFC headlights would fit our buckets - seems the Bobber ones do, and appear the same as the TFC ones Thanks to Stephen cotter for being the Guinea pig Triumph part number A9830104 But at $620...... each....... Triumph Motorcycles | Part Search |...
www.r3owners.net
Oh and given your year you should do the headlight relay installation. E.g. Eastern Beaver do a kit.
The LEDs will draw much less current but still worth doing it. Avoid possible future ignition switch breakdown.
Also the old original headlights will be a little brighter on their own just by doing this relay job.