I always think of 扉 as sliding doors (as also usual in trains and buses), and of ドア as a door with hinges (or some other more modern/Western construction, like elevator doors).
See 類語例解辞典《小学館1994,2003》
① 「扉」は、[蝶番]{ちょうつがい}などを軸に回転するようにして開閉する機構のものも左右に開閉するものもいう。
(「扉」 is used for both doors with hinges and sliding doors)
③「ドア」、主に[蝶番]{ちょうつがい}で開閉する機構で洋風のものをいうが、「自動ドア」の場合は、左右に開閉する機構であるのが普通。又、「ドア」は、出入り口以外には使わない。
(「ドア」: mainly for doors with hinges; except for automatic doors, here it is common for sliding doors as well; only used for entrances/exits)
I suppose, when thinking of a western-style door, one associates it with ドア first, as it has got the more specific term ドア. Thus, 扉 is associated especially with sliding doors, in contrast to ドア. But as a general term, 扉 may refer to other kinds of doors, as evidenced by the [広辞苑]{こうじえん} definition [開]{ひら}き[戸]{ど}の[戸]{と}, and 扉 comes from [戸片]{とひら}.