@RobedActor77417 Erick's suggestions are spot on and I just wanted to add some intermediary steps in case you can't equip a Nemesis quite yet (or need more badges).
For katana, at Lvl 60 you should be able to equip a Sigma Seigan from the Player Shop. From there I'd start working on the Saika Revolsio from the 13* Collection Folder (next to Koffie at Gate). Then I'd move on to the Nemesis Cougar from the unique weapon badge shop.
The Sigma Seigan is nice because it has a Dex requirement (assuming Dex mag) and a decent potential (crit rate and dmg up). You can also enhance/grind it to +26 without "wasting" resources, or go to +30 for a little more dmg from unlocking the Lvl 3 potentional. I say going to +26 isn't a waste because a 12* weapon at that level can fully enhance a 13* from 0 to 10 by itself. This means you can use it later to jump your Nemesis Cougar to +10 as soon as you get it.
The Saika Revolsio also has a Dex requirement and by completing the collection folder you'll get it at +30 with decent enough affixes for no meseta at all! However, I recommend completing at least 2 weapons from this Collection Folder because later it'll take 1 to instantly enhance your Nemesis Cougar from +10 to +20, and a second to take it from +20 to +30 (no additional fodder necessary).
You'll get the Nemesis Cougar from the unique weapon badge shop and may eventually want to grab a 2nd so that you can max the elemental dmg (keep an eye on the Player Shop prices if you need badges for other things like your bow). You definitely want to enhance this one to +30 to max the potential (17% extra dmg) and we outlined how to do this efficiently using your old weapons.
Unfortunately, I main katana so my bow knowledge is lackluster and I can't get the Argus guide to open at the moment. So take this all with a big grain of salt but, I think the Raven Feather is preferred to the Cougar Feather because you weave in normal attacks via rapid fire for PP regen as a bowman. Either way, you get the Raven/Nemesis Feather from unique weapon badges and you'll definitely want to get it to at least +30 and max element (60) as it's your main weapon.
Until then, the Sigma Branch is probably a safe 12* option, though I was using the Rikauteri around your level (also from unique badge shop). The one nice thing about Sigmas and Rikky is that they're All Class bows which means you can level your other classes with it by using BR as a sub. I used the Yamigarsu (all class Katana) this way to quickly get the Lvl 75 class bonuses while running Tokyo keys. However, Rikky probably isn't optimal for a Bow main as the potential from something like Dalz Varley may be better if your skill tree is invested in Rapid Fire. The problem with Dalz is that it came from the astracite shop after beating Luther a bunch, so you'd probably have to check the Personal Shop nowadays.
The Ray Bow is also decent investment as a stopgap between your 12* and the Raven/Nemesis Feather. You can get the Ray Bow from the Rising Weapon Badge 2 (RWB2) shop and you get RWB2s by earning the seasonal weapon badge (RWB4s atm) and then exchanging them for RWB2s at the weapon badge shop (via a generous exchange rate). The reason this can be a good investment is that when you combine 6 copies of the Ray Bow from the shop you'll unlock the ability to enhance it to +35 instead of the +30 default. And at +35 weapons gain access to their SAF which you can see by clicking "Check Augment Factor" when selecting a weapon in your inventory. What's really nice is that SAFs transfer with 100% success when affixing onto the same number of slots! And the SAF for the Ray Bow is called Astral Soul which happens to be an endgame augment that gives +35 all atk, +35 HP, and +5 PP. However, unless you have tons of badges, I'd probably save this SAF for affixing onto whatever 15* weapon you decide to go for eventually.
Lastly, I just wanted to follow-up on weekly meseta farming. If you haven't yet, I'd suggest making 2 more free characters and getting them to Lvl 50 so you can do the 1M weekly quests (+ 3x the Yerkes and Bar Lodos money each week, as well as 2 more silver Tokyo keys a day + 2 more gold ones each week for leveling main char.). I know setting up new characters can be daunting, but it's much easier if you make them BR/RA as well because you can give them your old gear immediately and there's no learning curve. The intro quests (e.g. Afin, Jan, and Casino quests) + Cressida's pebble/stone quests near the bottom of her page (necessary quest materials on player shops) will get you close to Lvl 30 within an hour or so and then you can also save the EXP tickets they're giving out now to power level to 50. From there you can knock out your dailies for both extra characters in about 10min total (here's one example of a fast daily loop https://youtu.be/ss7Blh9g9LA).