So to start you are playing a champ that is hard to carrying with. She goes in to fights and tends to get screwed after killing her target. I would suggest learning someone with a better all in pattern like akilla. That said i am sure you are going to reject this advice, so moving on.
So next you need to talk about theory crafting. You build is missing a key factor for every dia player needs, CDR. CDR is so important on DIa. Your Q cdr is your gate ability for your mobility and damage. Try replacing lich with a nashors. You do lose your auto burst but you get sustain AP on hit. Plus the 20% cdr really helps.
Dia is not a late game champ. She is also not very forgiving if you make a mistake. The fact that you are getting 20+ kills in your wins says you are waiting to win. What do you do after you get a kill? Are you looking for more kills or are your trying to get a tower? Just taking kills through out the game does not win it for you.
From your stats your skills seem to better than most bronze........not saying much i guess. If you want to get out of bronze you need to make sure you are taking objectives your self. Dia is a really good split pusher and tower taker. Normally I would not tell you to split push to win. Though in your case till your MMR raises a few levels it might be justified. Ward heavily where you are going to split pushing and draw the enemy to you and let your team take easy team fights. If the enemy only sends one 1 person kill them and keep marching forward.
Also start trying to steam roll top. ADCs are not as great mid game anymore. It is harder to get them rolling compared to the top laner.
I actually play Dia ranked when forced mid. It is a comfort pick for me since i picked her up season 2.