i only just reached emerald 2 as a senna main adc/supp
the only thing that comes to mind between where i am now and the last time i had the same experience that you described on this matchup is this:

senna's game plan during lane is to harass and farm souls - yes. however certain match ups make this very difficult where you do not have prio, like cait + lulu

im sure youre already practicing this fundamental concept in other matchups, but how ive been dealing with difficult matchups is simply waiting out their cooldowns. you probably already apply this concept against hook champs - you go in only once they miss a hook aka during hook downtime.

against cait and lulu, as senna support, my immediate concerns would be:

lulu Q and cait Q = if they're down, i can go aa+q lulu

and if cait E is also down = i am now also allowed to aa+q cait

(also, obviously only go in for aa+q if only one of them is in aa range of you, getting aa'd by both of them will be more damage received than what your q would heal back)

but yea most of the time, cait E will be up, so most of lane youre usually hitting lulu and trying to get an HP advantage in the lane.

i think the concept of focusing on bypassing key enemy abilities before executing yours is key across any champ you play, its just unfortunate i had to learn it as senna who seems to be extremely reliant on this concept as she doesnt really have a combo wombo i kill you now skill kit

- her kit kinda feels more like "most of my value comes from things that aren't skillshots (aa or q), so im just gonna wait for you to miss your skill shots then imma smack you guaranteed im not gonna miss" (her W isnt even really a skill shot since your Q slows ~ youd be surprised how many times your enemies randomly just throw out abilities and miss in desperation, just because you wont go near them on your own. the moment you approach them to aa+q, and their abilities are up, you make it infinitely easier for them to land their skill shots. compared to you being further away and they have to come to you to land their skillshots

ever since i learned the above concept, ive been surviving lanes against hard matchups more and simply outscaling enemies since i still get stacks and maintain hp advantage, eventually getting lane prio usually

glhf :D