Should I ask him out? how should I ask him so that I don't sound desperate or chasing after him?

i met this guy like 6 weeks ago, the first time we met he hang out around me, like very interested. after we hang out every weekend with the same friends, he is very shy, but he always stayed around, get me drinks and even saw me off and kissed me. however he never took the initial to text me first, but he added me in Facebook. when i texted him he replied really nicely and still sounded like intersted. i asked him if he could help me with my math test, he said he could. after i texted him when he has time, he didn't reply. then i texted him that i was disappointed that he my message was unreplied, he said sorry that he been working late, forgot to reply, and he has no time this week to be honest (he actually works too much, and sometimes is off at 11pm). the next day we were going to a fun bar with friends, a week before he told me he wanted to come, so i texted him that's we were going there thst he could join as well, he didn't reply (i suppose he was working late or msybe as he said he was busy the other day ). i saw him again on the weekend, he was still nice to me and asked like how was my week etc, like wheather i am in town for Christmas, and said like let's travel whatever. but he left really early and told me that he had to ho.
i am a bit confused if he is avoiding me, or what? he is always very nervous when talking to me. i really like him, and wanna spend more time with him, but i don't know how to ask him out as he didn't reply my kast message. i feel a bit awkward about it. also i am wandering if he didn't rrply on purpose or just forgot.
Also my friend that knows him too, is organizing a bar crawl this weekend, and invited me, and a lot of other people too... He never been to that district and before was very curious, so i do not know if it is ok to text him and ask if he is interested to join. or how should i do it?


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