I am playing a rogue who chose the archetype Arcane Trickster, which means I can cast spells.
Can I make a normal-range or close-range attack for my main action, and as a bonus action cast a spell that requires 1 action (e.g. chill touch or fire bolt)?
You cannot use your bonus action to cast a spell - unless it is explicitly stated that the spell's casting time is one bonus action.
On any given turn, you may take one Action and One Bonus action. An action can be one of various things, but is usually either attacking with a weapon or casting a spell.
A bonus action is very different to a normal action. You can only use a bonus action if you have a feature, spell, magical item, etc. that requires a bonus action to use. For example, as a rogue, your 'cunning action' feat which you get at 2nd level allows you to use your bonus action to use the dash, disengage or Hide actions (which normally take a full action to perform).
A spell with a casting time of one action can only be cast as an action, not as a bonus action.
See the basic rules for casting time:
Most spells require a single action to cast, but some spells require a bonus action, a reaction, or much more time to cast.
A spell specifies if it has a casting time of one action or one bonus action.
And the basic rules for bonus actions:
You can take a bonus action only when a special ability, spell, or other feature of the game states that you can do something as a bonus action. You otherwise don't have a bonus action to take.
You can only use a spell as a bonus action if it has a casting time of one bonus action.
As the other answers correctly note, in general this cannot be done. Actions are actions, and bonus actions are bonus actions. You can only take a bonus action if a spell, feat, feature, or similar explicitly says you can-- otherwise, you don't have a bonus action to use.
There are a couple of exceptions, in this case the PHB Sorcerer class and the Order Domain Cleric (Guildmaster's Guide to Ravnica) (h/t to Medix2 for the Order Cleric example).
Sorcerers have a special resource called sorcery points, and at level 3, sorcerers can take two metamagic options. One of these, Quickened Spell, allows the sorcerer to spend two sorcery points to cast a spell that normally requires an action to cast and instead lets them cast it as a bonus action.
The Order Cleric gains a feature at level 6, Embodiment of the Law, which allows them to cast an enchantment spell of first level or higher, and which normally has a casting time of one action, as a bonus action instead.
