High attack bonuses are possible
This is dependent on level and magic items. It is also dependent on the target's AC. A rather high modifier can be obtained with +6 proficiency, +5 dexterity, archery fighting style, a +3 bow, +3 ammunition, and ioun stone of mastery for a total of +20, making a attack roll result of at least 22 (a 1 misses anyway, vide Supra), sufficient for AC 17 with Sharpshooter. (But see note below). Further increases can be achieved using epic boons. Other bonuses such as bardic inspiration are also useful, but those rely on limited resources running contrary to the desire to always hit.
The maximum possible modifier on your current level is of course lower, even with appropriate magic items (which are probably difficult to come by, especially so at level 6). With +3 proficiency and +4 Dex you can have only +16 with the calculation above.
In 5e missing is always possible
Like a rolled natural 20 will always hit, a natural 1 will always miss. Therefore, even with a very high modifier, there is a 5% miss chance. Of course there are features which allow rerolls. For example the Halfling's Lucky allows rerolling a 1 once. This with a very high modifier would mean that only one in four hundred attacks would miss. It is not a human however and it does not let you avoid rolling entirely. [Incidentally, a halfling also cannot efficiently use a longbow.] There a ways to avoid the attack roll entirely, such as the clockwork amulet or the rogue's stroke of luck. These cannot be used consistently however.
Also, in 5e, there are no basic rules which would make a bow break.