What you describe is my preferred style of play, and the key point is fairly simple:

You don't need to keep the world under constant threat, and the PCs don't need to be adventuring 24/7/365.

Indeed, trying to do so has led to many people over the years observing that, once play begins, characters tend to grow in ability ridiculously quickly relative to the passage of game time - after spending 30 years to reach level 1 (i.e., the character's starting age is 30), they then hit level 5, or 10, or 20 within a matter of weeks or months.

Instead, don't just allow time for the PCs to travel from one adventure site to the next, give them downtime as well, so that they can spend some time at the home base, building it up and interacting with the others that live there. If you're comfortable with lower-key activity, you can also run "day in the life" sessions depicting these activities, which is where the players will really start to feel a connection to their characters' home base.

So how frequent should adventures be? That's largely up to you and your group, of course, but I can offer a couple examples from games that are designed for this style of play:

• Ars Magica is probably the granddaddy of RPGs built for long in-game time scales. Everything happens on a timetable of seasons here, including character advancement - if you want to get better in combat, you spend a season training. For an "average" campaign pace, the latest edition of Ars Magica recommends having one adventure every 1-4 seasons, although my memory of previous editions was that 1d10 seasons between adventures was once the norm.

• Rei Arthur Pendragon is designed around the pace of life in the times of Arthurian legend. As such, each year sees characters going on one adventure, usually in spring and/or summer, then returning to their lands and spending the winter at home.

Why are you putting things so far from home?

If you want a home base to be useful, then you should put the adventures near it.

If you want a campaign travelling to the four corners of the world, make the home base mobile (or don’t have one in this campaign).

Just skip ahead to after the travelling.

Travel time can indeed bog down play time, so I advise just skipping ahead. The Basic Rules describe the speed of travel paces, so you can just skip ahead the amount of time it would take to complete the journey, or until the next event takes place.

If something is intended to occur on the road (or if you want to use random encounters in a hostile area), you instead say something like, "after travelling for about a day, Caorlis (the party ranger) notices some branches that seem to be out of place standing upright on the woodlands to either side of the road. You suspect something disturbed these branches" to hint at an ambush detected by a high passive perception.

Show them the consequences of travel time

If long travel times to destinations that aren't important to the story line becomes frequent, you can clue the party into the consequences of this activity using a bit of narrative techniques. The next time they travel to an area they could have helped if they were near by for someone to give notice to them, have them return to the ruins of a village. This is especially powerful if you had been foreshadowing an attack for some time (whether or not they picked up on the clues).

Perhaps they track down a few survivors in a nearby cave who angrily say, "where were you! We tried to find you when the king's spies told us an attack was coming, but you were gone. We could've used your help." This demonstrates the importance of staying near the action of the story.

Why do they go there?

While I fully agree with Resposta de David Coffron, there seems to be a different problem here. Namely; why do they want a home base?

If they have no reason to go there why would they? Maybe it has some financial benefits or you're planning some sort of story with their home at its center. What happens there isn't important as long as they have a reason to go.

As an example I'll give you something out of my current campaign: We've recently started building a town, and some tention has risen with the local lords. They seem to be dead set on stopping us from becoming succesful, even going so far as to send troops. This all lead to a massive battle between our characters and our Construct army (because why not) and the local lords. Our original incentive for the town was simply to store our goods and get a bit better profit for our goods, but this all lead to an epic campaign!

Most importantly; it is up to you, the DM, to make sure that they can do everything you want them to in the time they're given. They have three weeks to stop the Big Bad? Make sure they're within range. Who knows, maybe they'll avoid this whole problem and hire a bunch of wizards to teleport them all over the world.