The 2003 BMW 1150RT is difficult bike to buy an alternator belt for.
The problem is-- the alternator pulley & belt design was changed in late 2003 production (July 03 or so) so unless you know what alternator pulley you have, or the bike's build date you really don't know what belt it requires.
The easiest way to determine what belt it takes (and the proper belt adjustment procedure) is to simply remove the belt cover & look to see what alternator pulley it has.
If a free wheeling (over-run) pulley then it takes the Elastomer belt, if a non free wheeling pulley (conventional solid bolted up pulley) then it takes the older Poly-V belt.
Type of belt also determines the adjustment procedure-- If the old poly-V then belt tension is the proper way (that's in you new manual).
If the newer Elastomer belt required then that is adjusted by the pulley spacing distance (not tension). (this isn't in you manual & if you are installing the Elastomer belt let us know & I will give you the pulley spacing distance)
There is (was) a way to tell belt type by front belt cover markings but that isn't always accurate as the front cover might be a replacement.
In any case-- If installing the Poly-V then you can set the belt tension using a torque wrench on the BMW special adjusting nut-- OR simply use a cheap M-8 acorn nut
on the exposed adjuster stud.
Or if experienced with belt tension feel-- you can set the belt tension by CAREFULLY prying up the bottom of the alternator then checking the belt tension with a 90° twist (you need a good base feel for this method though). If using this method you need to be VERY CAREFUL to not damage the wiring running under the alternator
If your bike takes the Elastomer belt then neither the special BMW adjustment nut or the acorn nut will do any good as the belt tension is just way too high for either to work.
On the Elastomer belt, I set belt pulley spacing with a tool I made to force the pulley's apart to the proper spacing. Some do it by prying on the bottom of the alternator to a pre marked alternator position but that is risky due to the belt tension required & soft alloy alternator housing.
I have seen quite a few of the Elastomer belts set incorrectly due to the belt installer trying to use the old torque method, or simply thinking the tension required to set properly feels way to high to them (those Elastomer buggers are REAL tight at proper install tension).
As for doing anything else while in there?-- not much to do other than look for oil leaks & visually inspect the area.
That alternator is a REAL PAIN to remove to replace any parts on it as it comes out the rear so the ABS system, Motronic, etc needs to be removed first. Just give the alternator shaft a spin & if the bearings don't feel rough, gritty, or growl then don't mess with it.
Added: Free wheeling pulley shown below---