Infinity Edge is balanced around the fact that you need to build two crit items before it is useful, making it a viable option for a three-item powerspike for Marksman.
But on Senna you only need 80 souls (as a support I ususally hit ~90 at 20 min) to get 40% crit, making IE viable as a second item, making Senna pop of earlier than with a conventional crit build and scale better than with a popular lethality build.

I am a support main and this build is created for supports, but you can also play it as a fasting ADC with a melee farming support (Tahm Kench/Wukong/Orn).
It is also possible to play it as a farming Senna in the midlane, but in this case you might want to swap Muramana with Infinity Edge if you can't hit 80 souls on your second Item completion (since the soul droprate decreases if you last hit the minions).

You absolutely need the Precision tree as primary for the HP and mana sustain: Fleet Footwork to heal yourself and Presence of Mind to manage your mana.
As a third rune I recommend Legend: Bloodline for even more sustain, but Legend: Tenacity is also a viable option into heavy cc-teams; but don't opt for Legend: Alacritty, since your attack speed scaling is terrible (30% effectiveness).
As a last rune from the primary tree I recommend Cut Down, but Coup de Grace is also solid if the enemy team has no tanks.

As a secondary tree you need Inspiration for Approach Velocity to catch up to people.
The second choice should be Magical footwear for free boots and a little extra movespeed.
Technically you could choose Perfect Timing, but I feel like this clutters your inventory too much, especially as a support when you also need to have Control wards and the Support Item on you.
As shards you should take AD/AD/armor. Don't take attack speed here out of the same reason you don't want Legend: Alacritty.

Your core items are Eclipse for Lethality, armor pen and max HP damage, Infinity Edge for more crit damage and Muramana for a little onhit and a lot of AD (and Mana as a nice bonus).
This works because Senna's passive gives her enough crit chance for IE to work (provided you can collect at least 80 souls, which I consitenly hit before I complete my second item).
This creates a 2-item powerspike for Senna (and not at least 3 items like with other crit builds) but you scale way better than a lethality build which falls off once the enemies start to get some armor.
If you are only into squishies, you can swap the Eclipse for a Duskblade of Draktharr.
For boots you basically always want swifties to make kiting easier, since you are really squishy. Mercury's Treads and Plated Steelcaps are only viable if you are into a full AP or AD team.
Further item options are:
- Rapid Firecannon cause the extra range feels like cheating
- Zhonya's Hourglass if you are getting focussed
- Serylda's Grudge if the enemy has a lot of armor. Also the slow on you autos feels great
- Lord Dominik's Regard if the enemy has a lot of health and armor (usually you should choose Grudge though)
- Mortal Reminder if you need antiheal
- The Collector of you just want more damage

You need to max Q for sustain and slow.
Afterwards you can max W for longer roots but I prefer to max E for better mobility and kiting.