I get that at some point you might want more than "just" tickling.
Well there's like a million ways you can go, but remember all of them have to be decided by both of you, pushing could go terribly wrong.
That being said all of it depends on the personalities of both you and your partner.
I will describe a few examples from my current relationship as yours seems to be similar to when we started out.
Partial bondage worked great for us, when we first started.
Just tying one arm gave her the feeling to be able to still somewhat defend herself, while making it easier for me to pin her down/access some tickle spots.
From there you can slowly increase the level or just mix things up.
If that is too far already then you can try to start with a blindfold.
Rolesplays also are a good way to take things further. And it doesn't have to be the typical cliche's as they can be hard to pull off and thus feel awkward.
What works best for us is being spontanous and me slipping to an (playfully) evil persona, while my girlfriend switches to a more submissive persona.
E.g.: Punish my girlfriend for things she might or might not have said or done during the day. (The reason can even be an outright lie)
Not immediately letting her go after an agreed period of time, instead continuing to tease and tickle her.
Demanding impossible tasks, like keeping silent or the arms above her head while not holding back at all and punishing her when she fails.
Stuff like that.
Also nice to try, tickle bets. Those work great both with or without bondage.
If she wants something minor from you (or just come up with a "prize" on the fly) make her work for it.
Try to find out, what and how long your partner can and is willing to take before giving up. Try to keep her on the edge of that. She should have a fair chance to win, but make those victories hard earned.
Examples are having to endure a certain amount of time, having to keep silent, not moving when certain body parts are tickled, ...
Last but not least, not exactly bedroom stuff but still interesting: public or hidden tickling. Can be used as some kind of early foreplay.
Examples are having my hand on her hip or knee, where nobody can see it. Or if there's a blanket on the table, having her foot on my lap. Then without anybody noticing, I slightly tickle her. It's so much fun watching her struggle trying to keep her composure. Don't overdo it though unless she's okay with being exposed in the public. So far we were not spotted by anyone, at least not that I know of.