Guys, Would you feel bothered if a girl texts you like this?

Sil01courious
Does it annoy guys to receive a text from a girl occasionally, to share something funny we had an inside joke about and if I ask him how his work is going?
To give some context: I started becoming closer to a guy from work but now we won’t see each other for a month. I know that if I have an interest in a guy I should also express myself, and I’m very shy to talk to men in general. But I’m trying to establish some contact and show some interest, I just don’t know if I might be bothering him.
Guys, Would you feel bothered if a girl texts you like this?
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