how do i show her im not clingy?

well my girl is a year older and very sporty she works and plays sport this take up almost all her time. i work also but i still have time to socialize and all with my mates too but i just want to spend time with her cuz i love her, she thinks im CLINGY because i always ask her if shes coming out or if she wants to do something like the cinema or play some football, she always says no which then annoys me and she gets pissed off because i would ask her to come out.

there is nothing wrong with a guy wanting to spend time with his girlfriend if they don't see each other as much anymore but she thinks other wise not long ago she complained to me about texting to much but i only text her to see how she is whats new and all but she thinks i text to much and i already told her that's why i do it because i don't see her as much :(

WHAT SHOULD I DO ??? i love her to bits and i don't want this stupid thing to ruin it !