Your question was: How to have better conversations with bf.
Aligning with someone mentally, emotionally, spiritually and physically isn't always easy. Open, inquiring attitudes and an original point-of-view are usually what leads to meaningful and interesting discussionson any topic...(aesthetics, ethics, politics, feelings, religion, etc). Listening and being interested is key also. However, he's partly responsible for starting a meaningful conversation as well...
Cl-itwinflame is correct that your BF also contributes to your conversations, or lack thereof. Did he mention the topics or types of "deep" conversations he'd like to have? A thought: if you watch the news together then you could talk about some of the items mentioned on the news and go a little deeper, like where you two stand on issues. Or, if you two go to the movies together you can talk about what you thought of the characters, the plot, or about what the characters faced as a challenge in the movie. Because you are shy things need to come naturally otherwise it will look forced. That is why I suggested piggybacking these types of conversations to what you do together.Just be aware of one thing - as you two discuss ethics,morals or scruples you may discover that you grow closer or you may realize you are not a good fit. Many times people dont like talking about serious or intense issues or subjects because then others will see them for who they are and/or maybe they'll realize they really dont like their SO.
To find out that your SO is okay with dogs getting electrocuted for fun or that he or she doens't see what the fuss is about kids being left alone in a hot car for hours...can be horrifying, but it is much better to find out earlier than later...
The two of you should do new and different things together - sharing experiences helps enliven the relationship. It's easy to get stuck in the humdrum same old, same old. And why don't you ask him about some of the deep topics he wants to talk about... and begin a discussion..
And both of you together and separately want to be engaged in the world -paying attention to what's going on in the world, taking classes, seminars, enriching yourself, etc..
He's probably afraid of becoming stagant. And you're afraid of not measuring up. But you're not giving yourself enough credit! It's not about wanting deeper conversations to please your boyfriend but to allow yourself to grow as a human being yourself.
That is not the same as twisting yourself into a pretzel to make him happy. You need to be true to who you are!.
I just bought "The Book of Fabulous Questions: Great Conversation Starters About Love, Sex and Other Personal Stuff" by by Penelope Frohart.It's got a bunch of simple questions, ranging in 'seriousness' from "what's your favorite color" -type questions to more serious and provocative questions towards the end. Fun party book, or fun for the 2 of you to just pick a few questions and answer for each other. Some of the questions can spark some serious conversations...