Much scholarly literature has already been written regarding the placement of Shavuos between the Parshiyos of Bamidbar and Naso. So who are we to suggest other explanations? But we will nonetheless make an attempt.
Regarding why Shavuos is next to Bamidbar, Tosfos in Megilah 31b writes that Atzeres (Shavuos) is specifically after Bamidbar and not Bechukosai in order that that curses in Bechukosai should not be immediately juxtaposed to Shavuos. We see a clear reason why Shavuos comes after Bamidbar.
(For more explanation on the deeper connection between Bamidbar and Shavuos, see Drash Moshe on Parshas Bamidbar)
But what could be its connection to Parshas Naso?