Asbo, I hope that you aren't implying that you want to get rid of this live-in BF via deception. I assume you want to go another route: genuine.

So, be a guy that she wants. To increase your chance of achieving that, what is it she wants? Behave as that guy (DISCLAIMER: clearly if what she wants is too far a leap from who you actually are at your core, then give up with this women before it ends in tears).

What to do / What is it she wants?

I assume that she is already attracted to you. If not, your post was wildly premature (!)

Since you are looking to create a longer-term thing, and since you wish to give out a "I like relationships" vibe, then ask:
"what are you looking for in a relationship?"
Then ask her to rank in priority (A, B, C).
Then later on during time together repeat back to her that you guys are so good together as you have: A, B, C.... you must have demonstrated or talked about some of these values/actions before this.
While doing the above don't come across as needy, instead be relaxed, smile, keep it fun!

There are no silver bullets for this, the above is just one small nugget.

What not to do

You also must know by now why she doesn't like ex-BF, so don't do these things.

To utilise one of Knave's infamous statistics, a 38.34 % chance