No, Bulbasaur and its evolution were always Grass/Poison types. The only Pokémon introduced in Gen I that went from a single to dual-type Pokémon are Magnemite/Magneton (Electric -> Electric/Steel) and Jigglypuff/Wigglytuff (Normal -> Normal/Fairy) respectively, upon their secondary types introduction. Otherwise, all other Pokémon that are dual-types in Red/Blue were from the start.
However, it's very easy to mistake that dual-types never existed in Gen I, or that Bulbasaur was solely a Grass type. For Bulbasaur specifically, besides Rowlet, it is the only unevolved Starter Pokémon to have a second type, having made it an odd exception for many generations. For all Pokémon in general, these are the most plausible reasons I could come up with,
Dual-type Damage Misinformation Glitch - In Generation I, a major glitch resulted in the wrong type effectiveness message displaying against dual-types. Pokémon with two types with a weakness or resistance to the same type receive neutral damage, but the incorrect message would be displayed. For instance, Grass-type moves would display as "not very effective..." against Gyarados, despite it dealing neutral damage. The game prioritizes which message displays for each scenario where neutral-damage is dealt, returning an incorrect message as a result. Additionally, if an attack is super effective or not very effective on one type and deals no damage against another, such as using Earthquake on Charizard, it will display that the attack missed. This could reasonably make someone believe that Gyarados was Dragon-type, or Charizard is pure Fire-type. The priority of messages can be found here.
Media surrounding the games - Most media released during the time of Red/Blue never referred to Pokémon as having multiple types. During the early seasons of the anime, it’s not often a Pokémon’s type is ever brought into conversation, though when it is, it’s only one of the two it actually has. The manga, as OP mentions, has errors that mistake a Pokémon’s type. The TCG didn’t have dual-type cards until Gen III.
Pokémon Type Distribution in Kanto - With odd dual-type Pokémon distribution, there is questionable enough type distribution in Gen I that it'd make sense for people to mistake there being no dual types. Normal types only other secondary type in Gen I is Flying, Ghost and Dragon types exist for only one evolution line, Electric and Fire-type Pokémon have only one or two dual-type Pokémon, most Grass-types are Grass/Poison, there are no single-type Ice or Flying Pokémon, etc.
Despite these reasons, it’s plausible for people to mistake the introduction of game mechanics from a 30-year old franchise. Many people forget that, for instance, the Physical/Special split was introduced in Gen IV, or held items existed since Gold/Silver. It’s reasonable to assume that people could simply forget mechanics from such an old game.
