Both words you mentioned have Kanji.
海豚{いるか} - dolphin
蜜蜂{みつばち} - honey bee
Most biological terms are written in Katakana in everyday language (places like aquariums and TV spots).
However it is also not uncommon to see them written as Kanji in biological or science texts.
Other examples include...
-海豹{あざらし} (アザラシ) >[Earless Seal]
-海驢{あしか} (アシカ) >[Eared Seal]
-膃肭臍{おっとせい} (オットセイ) >[Fur Seal]
-蜻蛉{とんぼ} (トンボ) >[Dragonfly]
-水黽{あめんぼ} (アメンボ) >[Water Strider]
EDIT: The list you provide I have usually seen as the following.
赤ん坊(a baby is an animal?)、イルカ、うさぎ・ウサギ、蝸牛、狐、くらげ・クラゲ、トラ、トンボ、バラ、ミツバチ、山荒、寡婦(a widow is an animal?)、リス
Depending on where you are usually depends on how they are written. A children's science/biology centre will usually feature all names in ひらがな as some 小学生 aged children have not yet learned カタカナ. However family aquariums and zoos usually feature the 漢字 and カタカナ readings ie. 北極熊{ホッキョクグマ}.
Without knowing more about your list and the person who wrote it, it is somewhat difficult to know why they chose to put all except 2 items as hiragana. The choice whether to use ひらがな or カタカナ (or even Kanji) readings when referring to various animals is largely a stylistic choice by the author as both ひらがな and カタカナ can be read and understood interchangeably in this context. To cover all your bases (aand make it easier to search for), you could always have a third column in your database for カタカナ readings (instead of just ひらかな).
Some sources:
http://en.wiktionary.org/wiki/%E6%B5%B7%E8%B1%9A
http://detail.chiebukuro.yahoo.co.jp/qa/question_detail/q1319142318