Translation:Please take a shower immediately.
Also, apart from the difference in urgency 今 is a time word whereas すぐに is an adverb. So for example - 今 シャワーを浴びます - I will have a shower now - here, 今 indicates when you plan to have your shower - it refers to time only. Whereas すぐに シャワーをあびてください - please have a shower immediately - here すぐに is clearly describing the noun, ie. Don't wait, please go and have a shower right now!
right, to bathe is the act of washing yourself, i think they're thinking bath which is a type of bathing. basically this is saying to bathe (wash yourself) in the shower. plus culturally I've been taught that the Japanese typically don't actually wash in the baths, that's just for relaxing, showers (or buckets in more traditional places) are used to clean beforehand.
Without having seen the hints you're looking at, according to my dictionary, the kanji for 浴びる (あびる) means:
to dash over oneself (e.g. water); to take (e.g. shower); to bask in (e.g. the sun); to bathe in; to be flooded with (e.g. light); to be covered in
to suffer (e.g. an attack); to draw (e.g. criticism, attention, praise); to have heaped upon; to be showered with
So while it's been translated as "take a shower", it's not a 1-to-1 translation in Japanese.
It's a little tricky to explain in English but abiru means to pour over...? I can't think of a very good English equivalent but basically it's referring to you pouring the shower water over yourself - it doesn't really translate well to English. Pour not a great translation at all - can't think of another at the moment though. It goes with シャワー just like 入る goes with おふろ. It's pretty logical when you think about it - cos you literally get into a bathtub to take a bath and to have a shower the water showers down on top of you instead of you stepping into it. Also if you said シャワー you would be asking someone to give you a shower - like an actual physical shower head, thermostat, shower stall....
I think "shya-wa-" (no kana on phone!) means the noun, like the physical thing, the shower. So you can't say "the shower yourself"? So you use "abite" which means "wash with running water" as the verb and "shower" only add the noun. So "wash yourself in the shower". I think!